# Patent

## Title
Response calibration scheme using frequency-shifted stimulus signals

## Abstract

The response of a receiver is calibrated using frequency-shifted stimulus signals. A source provides a stimulus signal that has a non-zero bandwidth and an adjustable spectral position. A signal path coupled between the source and the receiver introduces distortion to the stimulus signal. The receiver acquires a first digital representation of the stimulus signal at an output of the signal path with the stimulus signal adjusted to a first spectral position and acquires a second digital representation of the stimulus signal at the output of the signal path with the stimulus signal adjusted to a second spectral position that is shifted from the first spectral position by a predetermined frequency offset. A processor, designates the distortion introduced to the stimulus signal by the signal path to be equivalent at the first spectral position and the second spectral position. The processor extracts a first combined frequency response of the receiver and the signal path at three or more frequencies within the bandwidth of the stimulus signal, and extracts a second combined frequency response of the receiver and signal path at the three or more frequencies and then determines the frequency response of the receiver from the first combined frequency response and the second combined frequency response. The response of the signal path is optionally determined according to the response calibration scheme under condition that the stimulus signal is known, characterized, designated or otherwise established.

## Background
BACKGROUND OF THE INVENTION
Many types of measurement and communication systems include a receiver coupled to a signal source through a signal path. Performance of these systems can be limited by amplitude unflatness, group delay variations and other distortion in the receiver or signal path. Typically, calibration schemes overcome performance limitations on the systems that are attributed to distortion. Known calibration schemes, such as those employed in dynamic signal analyzers, vector signal analyzers and other types of receivers, use the signal source to stimulate the receiver with a known stimulus signal. Response of the receiver to the known stimulus signal is determined and compared to a predicted response to correct for distortion introduced by the receiver. However, when the signal path coupling the source to the receiver introduces distortion to the stimulus signal, the accuracy of this calibration scheme relies on both the accuracy with which the stimulus signal is known and the accuracy with which the signal path can be characterized. There is a need for a response calibration scheme that does not rely on accurately determining the characteristics of the stimulus signal and an accurate characterization of the signal path.
SUMMARY OF THE INVENTION
In a response calibration scheme constructed according to a first embodiment of the present invention, the response of a receiver is determined using frequency-shifted stimulus signals. A source provides a stimulus signal that has a non-zero bandwidth and an adjustable spectral position. A signal path coupled between the source and the receiver introduces distortion to the stimulus signal. The receiver acquires a first digital representation of the stimulus signal at an output of the signal path with the stimulus signal adjusted to a first spectral position. The receiver also acquires a second digital representation of the stimulus signal at the output of the signal path with the stimulus signal adjusted to a second spectral position that is shifted from the first spectral position by a predetermined frequency offset. A processor designates the distortion introduced to the stimulus signal by the signal path to be equivalent at the first spectral position and the second spectral position. The processor extracts a first combined frequency response of the receiver and the signal path at three or more designated frequencies within the bandwidth of the stimulus signal, and a second combined frequency response of the receiver and signal path at the three or more designated frequencies. The processor then determines the response of the receiver from the first combined frequency response and the second combined frequency response. The response of the signal path is optionally determined according to the response calibration scheme under condition that the stimulus signal is known, characterized, designated or otherwise established. According to a second embodiment of the present invention, the response calibration scheme is implemented as a method.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows a system for employing the response calibration scheme constructed according to the embodiments of the present invention.
FIGS. 2A-3B show examples of frequency-shifted stimulus signals included in the response calibration scheme constructed according to the embodiments of the present invention.
FIG. 4 is a flow diagram of the response calibration scheme constructed according to a second embodiment of the present invention.



DETAILED DESCRIPTION OF THE EMBODIMENTS
FIG. 1 shows a system 10 including a receiver 12, a source 14, a signal path 16 and a processor 18. Response of the receiver 12 is determined according to the response calibration scheme constructed according to the embodiments of the present invention. The response of the receiver 12 is the frequency response, time domain impulse response, or any other response suitable for calibrating the receiver 12. The response of the receiver 12 is determined using stimulus signals S(f), S′(f) that are frequency-shifted relative to each other.
The source 14 provides the stimulus signals S(f), S′(f). The stimulus signals S(f), S′(f) have non-zero bandwidth and have adjustable spectral positions FC1, FC2. Examples of the stimulus signals S(f), S′(f) are shown in FIGS. 2A-3B. The stimulus signals S(f), S′(f) have continuous spectra as shown in FIGS. 2A and 2B. Alternatively, the stimulus signals S(f), S′(f) have discrete spectra as shown in FIGS. 3A and 3B, where the stimulus signals S(f), S′(f) are frequency combs with discrete teeth separated by a frequency spacing Δ. The stimulus signals S(f), S′(f) have the characteristic that the relative amplitudes and relative phases of spectral components within the bandwidth of the stimulus signal S(f) remain fixed whether the stimulus signal S(f) is in the first spectral position FC1 or in the second spectral position FC2 resulting in the stimulus signal S′(D).
Through the signal path 16, the stimulus signals S(f), S′(f) are coupled to the receiver 12. The signal path 16 has an input I coupled to the source 14 and an output O coupled to the receiver 12. The signal path 16 typically includes mixers, modulators or other active elements in combination with filters, transmission lines or other passive elements, and has a frequency response H(f) that introduces distortion to the stimulus signals S(f), S′(f). The distortion modifies the amplitude and/or the phase of the stimulus signal S(f), S′(f) between the input I and the output O of the signal path 16. The frequency response H(f), the time domain impulse response, or any other response suitable for calibrating the signal path 16 is optionally determined according to the response calibration scheme under condition that the stimulus signal S(f) is known, characterized, designated or otherwise established.
The receiver 12 is a dynamic signal analyzer, vector signal analyzer, heterodyne system, or other signal detection system, and has a frequency response G(f). The receiver 12 intercepts the stimulus signal S(f), as distorted by the signal path 16, and acquires a first digital representation Y1(f) of the distorted stimulus signal, with the stimulus signal S(f) adjusted to the first spectral position FC1. The first digital representation Y1(f) is a product expressed in equation 1.

Y1(f)=S(f)H(f)G(f).  (1)

The receiver 12 intercepts the stimulus signal S′(f), as distorted by the signal path 16, and acquires a second digital representation Y2(f) of the distorted stimulus signal, with the stimulus signal adjusted to the second spectral position FC2 that has a frequency offset δ from the first spectral position FC1. The second digital representation is a product expressed in equation 2.

Y2(f)=S′(f)H′(f)G(f).  (2)

In equation 2, the stimulus signal S′(f) represents the stimulus signal S(f) as shifted by the frequency offset δ. According to this frequency shifting, S′(f)=S(f+δ), indicating that the second spectral position FC2 is at a lower frequency than the first spectral position FC1. The frequency response H′(f) represents the frequency response H(f) of the signal path 16 also shifted in frequency by the frequency offset δ. Thus, H′(f)=H(f+δ), indicating that the second spectral position FC2 is at a lower frequency than the first spectral position FC1.

The processor 18 is coupled to the receiver 12. Typically, the processor 18 is a microprocessor or computer that is either incorporated within the receiver 12, or that is external to the receiver 12. The processor 18 extracts a first combined frequency response X1k of the receiver 12 and the signal path 16 at at least three designated frequencies fk within the bandwidth of the stimulus signal S(f). This first combined frequency response X1k=H(fk)G(fk), where k=0, 1, 2, . . . N−1, an integer indexing each of the designated frequencies fk.
The first combined frequency response X1k is obtained by normalizing the first digital representation Y1(fk) by the stimulus signal S(f) at the three or more designated frequencies fk. According to the normalization, X1k=Y1(fk)/S(fk), where S(fk) represents the stimulus signal S(f) at the designated frequencies fk. Alternatively, the first combined frequency response X1k is obtained by adaptive filtering to obtain a combined impulse response of the signal path 16 and the receiver 12. Mapping this combined impulse response into the frequency domain provides the first combined frequency response X1k at the three or more designated frequencies fk.
The processor 18 extracts a second combined frequency response X2k of the receiver 12 and the signal path 16 at the three or more designated frequencies fk. This second combined frequency response X2k=H′(fk)G(fk), where k=0, 1, 2. . . N−1, where H′(fk)=H(fk+1), indicating that the second spectral position FC2 is at a lower frequency than the first spectral position FC1.
The second combined frequency response X2k is obtained by normalizing the second digital representation Y2(f) by the stimulus signal S′(f) at the three or more designated frequencies fk. According to the normalization, X2k=Y2(fk)/S′(fk), where S′(fk)=S(fk+1). Alternatively, the second combined frequency response X2k is obtained by adaptive filtering to obtain the impulse response of the signal path 16 and the receiver 12. Mapping the obtained impulse response to the frequency domain provides the second combined frequency response X2k at the three or more designated frequencies fk. In addition to using normalization or adaptive filtering to extract the combined frequency responses X1k and X2k, cross correlation, cross spectrum analysis, adaptive channel modeling, and other known techniques are alternatively used to extract the combined frequency responses X1k and X2k.
The number and the spacing of the designated frequencies fk are chosen so the frequency response G(f) of the receiver 12 is determined to a specified accuracy. The accuracy to which the frequency response G(f) is determined generally increases as the number of designated frequencies fk increases. In an example where the stimulus signals S(f), S′(f) are frequency combs, the frequency offset δ between the first spectral position FC1 and the second spectral position FC2 is chosen to be equal to the frequency spacing Δ of the teeth of the frequency comb. Alternatively, when the frequency offset δ is not equal to the frequency spacing Δ, interpolation is used to acquire the first combined frequency response X1k and the second combined frequency response X2k at the three or more designated frequencies fk.
The processor 18 designates that the distortion introduced to the stimulus signal S′(f) by the frequency response H′(f) of the signal path 16 is equivalent to the distortion introduced to the stimulus signal S(f) by the frequency response H(f). This designation is achieved by equating the frequency response H(f) of the signal path 16 to the frequency response H′(f), where the frequency response H′(f) is shifted from the frequency response H(f) by the frequency offset δ. This designation results in the frequency response of the signal path 16 tracking the shifting of the stimulus signal from the first spectral position FC1 to the second spectral position FC2. FIGS. 2B and 3B show the frequency response H′(f) tracking the stimulus signal S′(f) when the stimulus signal S(f) is shifted between the first spectral position FC1 to the second spectral position FC2. Thus, S(FL1+kδ)=S′(FL2+kδ)=S(FL2+(k+1)δ) where FL1 represents a lower spectral bandwidth position when the stimulus signal S(f) is in the first spectral position FC1 and where FL2 represents a lower spectral bandwidth position when the stimulus signal S′(f) is in the second spectral position FC2. In the first spectral position FC1, shown in FIG. 2A and FIG. 3A, the stimulus signal S(f) has a spectral bandwidth that extends from FL1 to FU1. In the second spectral position FC2, shown in FIG. 2B and FIG. 3B, the stimulus signal S′(f) has a spectral bandwidth that extends from FL2 to FU2. Generally, the responses of the signal path 16 and receiver 12, and the stimulus signal are vector quantities having magnitude and phase components. FIGS. 2A-3B show the magnitude components versus frequency.
The processor 18 determines the frequency response G(f) of the receiver 12 and the frequency response H(f) of the signal path 16 at frequencies fk from the extracted first combined frequency response X1k and the extracted second combined frequency response X2k. A time domain impulse response, or any other response suitable for characterizing the receiver 12 is optionally derived from the frequency response G(f), based on known mappings between the frequency domain and the time domain. The frequency response G(f) of the receiver 12 is determined according to equation 3 and equation 4. The frequency response H(f) of the signal path 16 is optionally determined according to equation 3 and equation 4.

X1k=GkHk  (3)

X2k=GkHk+1  (4)

where Gk=G(fk), and Hk=H(fk).

Table 1A shows correspondence between the three or more designated frequencies fk, the extracted first combined frequency responses X1k, the frequency response Hk of the signal path 16 and the frequency response Gk of the receiver 12, in the example where three frequencies fk have been designated. Table 1B shows correspondence between the three or more designated frequencies fk, the extracted second combined frequency responses X2k, the frequency response Hk+1 of the signal path 16 and the frequency response Gk of the receiver 12, in the example where the three frequencies fk have been designated.












TABLE 1A









f0:
X10
G0
H0



f1:
X11
G1
H1



f2:
X12
G2
H2






















TABLE 1B









f0:
X20
G0
H1



f1:
X21
G1
H2



f2:
X22
G2
H3










The application of equation 3 and equation 4 provides the frequency response Gk of the receiver 12 at the designated frequencies fk. First, an initial designation or estimate is made for one of the frequency responses H0-HN of the signal path 16 at the designated frequencies fk. For example, the initial designation is made for the frequency response H0 of the signal path 16 at the first of the designated frequencies f0. Using the extracted first combined frequency response X10 at frequency f0, the frequency response G0 of the receiver 12 at frequency f0 is determined according to equation 3 as X10/H0. Using the extracted second combined frequency response X20 at frequency f0 and substituting the determined frequency response G0 into equation 4 provides that the frequency response H1 of the signal path 16 at frequency f0 equals X20/G0. Using the extracted first combined frequency response X11 at frequency f1 and substituting H1 into equation 3 provides that the frequency response G1 of the receiver 12 at frequency f1 equals X11/H1. Using the extracted second combined frequency response X21 at frequency f1 and substituting G1 into equation 4 provides that the frequency response H2 of the signal path 16 at frequency f1 equals X21/G1. Using the extracted first combined frequency response X12 at frequency f2 and substituting H2 into equation 3 provides that the frequency response G2 of the receiver 12 at frequency f2 equals X12/H2. Using the extracted second combined frequency response X22 at frequency f2 and substituting G2 into equation 4 provides that the frequency response H3 of the signal path 16 at frequency f2 equals X22/G2.
In this example, three designated frequencies f0. . . f2 are used to illustrate the application of equation 3 and equation 4 to determine the frequency response Gk. When there are more than three designated frequencies, the initial designation of the frequency response of the signal path 16 is made and equation 3 and equation 4 are similarly applied to determine the frequency response Gk of the receiver 12. Once the frequency response of the receiver 12 is determined, the response of the receiver can be calibrated by compensating for amplitude unflatness, group delay variations and other distortion in the receiver 12, that in the absence of calibration, can limit the performance of the receiver 12.
Under condition that the stimulus signal S(f) is known, characterized, designated or otherwise established at the frequencies f0-fN, the frequency response H0-HN of the signal path 16, determined through the application of equation 3 and equation 4, accurately represents the frequency response of the signal path 16. A time domain impulse response, or any other response suitable for calibrating the signal path 16 is optionally derived from the frequency response of the signal path 16, based on known mappings between the frequency domain and the time domain. Thus, the response of the signal path 16 is optionally determined according to the response calibration scheme. Once the frequency response of the signal path 16 is determined, the signal path 16 can be calibrated by compensating for amplitude unflatness, group delay variations and other distortion in the signal path 16.
FIG. 4 is a flow diagram of the response calibration scheme constructed according to a second embodiment of the present invention, where the response calibration scheme is implemented as a method 20. In step 21 of the method 20, the stimulus signal having non-zero bandwidth and adjustable spectral position is coupled to the receiver 12 through the signal path 16 that introduces distortion to the stimulus signal. In step 22, the receiver 12 acquires the first digital representation Y1(f) of the stimulus signal at the output O of the signal path 16 with the stimulus signal S(f) in a first spectral position FC1. In step 23, the receiver 12 acquires the second digital representation Y2(f) of the stimulus signal at the output O of the signal path 16 with the stimulus signal in a second spectral position FC2 shifted from the first spectral position FC1 by a predetermined frequency offset δ.
In step 24, the distortion of the stimulus signal by the signal path 16 is designated to be equivalent when the stimulus signal S(f) is in the first spectral position FC1 and when the stimulus signal S′(f) is in the second spectral position FC2. Designating the distortion introduced to the stimulus signal by the signal path 16 to be equivalent when the stimulus signal is adjusted to the first spectral position FC1 and when the stimulus signal is adjusted to the second spectral position FC2 includes equating the frequency response H(f) of the signal path 16 to the frequency response H′(f) of the signal path 16 as shifted from the frequency response H(f) by the predetermined frequency offset δ so the frequency response H(f) and the frequency response H′(f) track the shifting of the stimulus signal from the first spectral position FC1 to the second spectral position FC2.
In step 25, the first combined frequency response X1k of the receiver 12 and the signal path 16 is extracted at at least three designated frequencies fk within the bandwidth of the stimulus signal. Extracting the first combined frequency response X1k of the receiver 12 and the signal path 16 at the at least three designated frequencies fk includes normalizing the first digital representation Y1(f) by the stimulus signal S(f) at the at least three predesignated frequencies fk.
In step 26, the second combined frequency response X2k of the receiver 12 and signal path 16 is extracted at the at least three designated frequencies fk within the bandwidth of the stimulus signal. Extracting the second combined frequency response X2k of the receiver 12 and the signal path 16 the at least three designated frequencies fk includes normalizing the second digital representation Y2(f) by the stimulus signal S′(f) at the at least three designated frequencies fk. In addition to using normalization to extract the combined frequency responses X1k and X2k, adaptive filtering, cross correlation, cross spectrum analysis, adaptive channel modeling, and other known techniques are alternatively used to extract the combined frequency responses X1k and X2k.
In step 27, a frequency response of the receiver 12 is determined from the first combined frequency response X1k and the second combined frequency response X2k. Determining the response Gk of the receiver 12 from the first combined frequency response X1k and the second combined frequency response X2k includes designating or estimating one of the frequency responses H0-HN of the signal path 16 and solving for the frequency response Gk of the receiver 12 according to equation 3 and equation 4. Under condition that the stimulus signal S(f) is known, characterized, designated or otherwise established at the frequencies f0-fN, the frequency response H0-HN accurately represents the frequency response of the signal path 16. Thus, the frequency response of the signal path 16 is optionally determined through the application of equation 3 and equation 4 as shown in step 28. A time domain impulse response, or any other response suitable for calibrating the signal path 16 is optionally derived from the frequency response of the signal path 16, based on known mappings between the frequency domain and the time domain.
While the embodiments of the present invention have been illustrated in detail, it should be apparent that modifications and adaptations to these embodiments may occur to one skilled in the art without departing from the scope of the present invention as set forth in the following claims.

## Claims

1. A response calibration scheme, comprising:
a source providing a stimulus signal having a non-zero bandwidth and an adjustable spectral position; 
a signal path having an input coupled to the source, introducing a distortion to the stimulus signal between the input and an output; 
a receiver coupled to the output of the signal path, acquiring a first digital representation of the stimulus signal at the output of the signal path with the stimulus signal adjusted to a first spectral position, and acquiring a second digital representation of the stimulus signal at the output of the signal path with the stimulus signal adjusted to a second spectral position shifted from the first spectral position by a predetermined frequency offset; 
a processor, designating the distortion introduced to the stimulus signal by the signal path to be equivalent when the stimulus signal is adjusted to the first spectral position and when the stimulus signal is adjusted to the second spectral position, extracting a first combined frequency response of the receiver and the signal path at at least three predesignated frequencies within the bandwidth of the stimulus signal, extracting a second combined frequency response of the receiver and the signal path at the at least three predesignated frequencies within the bandwidth of the stimulus signal, and determining a response of the receiver from the first combined frequency response and the second combined frequency response.

2. The scheme of claim 1 wherein designating the distortion introduced to the stimulus signal by the signal path to be equivalent when the stimulus signal is adjusted to the first spectral position and when the stimulus signal is adjusted to the second spectral position includes equating a first frequency response of the signal path to a second frequency response of the signal path that is shifted from the first frequency response by the predetermined frequency offset so that the first frequency response and the second frequency response track the shifting of the stimulus signal from the first spectral position to the second spectral position.

3. The scheme of claim 1 wherein extracting the first combined frequency response of the receiver and the signal path includes normalizing the first digital representation by the stimulus signal in the first spectral position at the at least three predesignated frequencies and wherein extracting the second combined frequency response of the receiver and the signal path includes normalizing the second digital representation by the stimulus signal in the second spectral position at the at least three predesignated frequencies.

4. The scheme of claim 2 wherein extracting the first combined frequency response of the receiver and the signal path includes normalizing the first digital representation by the stimulus signal in the first spectral position at the at least three predesignated frequencies and wherein extracting the second combined frequency response of the receiver and the signal path includes normalizing the second digital representation by the stimulus signal in the second spectral position at the at least three predesignated frequencies.

5. The scheme of claim 1 wherein extracting the first combined frequency response of the receiver includes adaptive filtering the first digital representation and extracting the second combined frequency response of the receiver includes adaptive filtering the second digital representation.

6. The scheme of claim 2 wherein extracting the first combined frequency response of the receiver includes adaptive filtering the first digital representation and extracting the second combined frequency response of the receiver includes adaptive filtering the second digital representation.

7. The scheme of claim 2 wherein determining a frequency response (Gk) of the receiver from the first combined frequency response (X1k) and the second combined frequency response (X2k) includes designating one of the first frequency response of the signal path and the second frequency response of the signal path at a predetermined one of the at least three predesignated frequencies within the bandwidth of the stimulus signal, and solving for the frequency response (Gk) of the receiver using a first equation X1k=GkHk and a second equation X2k=GkHk+1, wherein k is an integer that indexes the at least three predesignated frequencies.

8. The scheme of claim 4 wherein determining a frequency response (Gk) of the receiver from the first combined frequency response (X1k) and the second combined frequency response (X2k) includes designating one of the first frequency response of the signal path and the second frequency response of the signal path at a predetermined one of the at least three predesignated frequencies within the bandwidth of the stimulus signal, and solving for the frequency response (Gk) of the receiver using a first equation X1k=GkHk and a second equation X2k=GkHk+1, wherein k is an integer that indexes the at least three predesignated frequencies.

9. The scheme of claim 6 wherein determining a frequency response (Gk) of the receiver from the first combined frequency response (X1k) and the second combined frequency response (X2k) includes designating one of the first frequency response of the signal path and the second frequency response of the signal path at a predetermined one of the at least three predesignated frequencies within the bandwidth of the stimulus signal, and solving for the frequency response (Gk) of the receiver using a first equation X1k=GkHk and a second equation X2k=GkHk+1, wherein k is an integer that indexes the at least three predesignated frequencies.

10. The scheme of claim 2 wherein the processor determines a frequency response (Hk) of the signal path from the first combined frequency response (X1k) and the second combined frequency response (X2k) by designating one of the first frequency response of the signal path and the second frequency response of the signal path at a predetermined one of the at least three predesignated frequencies within the bandwidth of the stimulus signal, and solving for the frequency response (Gk) of the receiver using a first equation X1k=GkHk and a second equation X2k=GkHk+1, wherein k is an integer that indexes the at least three predesignated frequencies.

11. A response calibration scheme, comprising:
coupling a stimulus signal having a non-zero bandwidth and an adjustable spectral position to a receiver through a signal path that introduces distortion to the stimulus signal; 
acquiring, with the receiver, a first digital representation of the stimulus signal at an output of the signal path with the stimulus signal in a first spectral position; 
acquiring, with the receiver, a second digital representation of the stimulus signal at the output of the signal path with the stimulus signal in a second spectral position shifted from the first spectral position by a predetermined frequency offset; 
designating the distortion introduced to the stimulus signal by the signal path to be equivalent when the stimulus signal is in the first spectral position and when the stimulus signal is in the second spectral position; 
extracting a first combined frequency response of the receiver and the signal path at at least three predesignated frequencies within the bandwidth of the stimulus signal; 
extracting a second combined frequency response of the receiver and signal path at the at least three predesignated frequencies within the bandwidth of the stimulus signal; and 
determining a response of the receiver from the first combined frequency response and the second combined frequency response.

12. The scheme of claim 11 wherein designating the distortion introduced to the stimulus signal by the signal path to be equivalent when the stimulus signal is in the first spectral position and when the stimulus signal is in the second spectral position includes equating a first frequency response of the signal path to a second frequency response of the signal path shifted from the first frequency response by the predetermined frequency offset so that the first frequency response and the second frequency response track the shifting of the stimulus signal from the first spectral position to the second spectral position.

13. The scheme of claim 11 wherein extracting the first combined frequency response of the receiver and the signal path includes normalizing the first digital representation by the stimulus signal in the first spectral position at the at least three predesignated frequencies and wherein extracting the second combined frequency response of the receiver and the signal path includes normalizing the second digital representation by the stimulus signal in the second spectral position at the at least three predesignated frequencies.

14. The scheme of claim 12 wherein extracting the first combined frequency response of the receiver and the signal path includes normalizing the first digital representation by the stimulus signal in the first spectral position at the at least three predesignated frequencies and wherein extracting the second combined frequency response of the receiver and the signal path includes normalizing the second digital representation by the stimulus signal in the second spectral position at the at least three predesignated frequencies.

15. The scheme of claim 11 wherein extracting the first combined frequency response of the receiver includes adaptive filtering the first digital representation and extracting the second combined frequency response of the receiver includes adaptive filtering the second digital representation.

16. The scheme of claim 12 wherein extracting the first combined frequency response of the receiver includes adaptive filtering the first digital representation and extracting the second combined frequency response of the receiver includes adaptive filtering the second digital representation.

17. The scheme of claim 12 wherein determining a frequency response (Gk) of the receiver from the first combined frequency response (X1k) and the second combined frequency response (X2k) includes designating one of the first frequency response of the signal path and the second frequency response of the signal path at a predetermined one of the at least three predesignated frequencies within the bandwidth of the stimulus signal, and solving for the frequency response (Gk) of the receiver using a first equation X1k=GkHk and a second equation X2k=GkHk+1, wherein k is an integer that indexes the at least three predesignated frequencies.

18. The scheme of claim 14 wherein determining a frequency response (Gk) of the receiver from the first combined frequency response (X1k) and the second combined frequency response (X2k) includes designating one of the first frequency response of the signal path and the second frequency response of the signal path at a predetermined one of the at least three predesignated frequencies within the bandwidth of the stimulus signal, and solving for the frequency response (Gk) of the receiver using a first equation X1k=GkHk and a second equation X2k=GkHk+1, wherein k is an integer that indexes the at least three predesignated frequencies.

19. The scheme of claim 16 wherein determining a frequency response (Gk) of the receiver from the first combined frequency response (X1k) and the second combined frequency response (X2k) includes designating one of the first frequency response of the signal path and the second frequency response of the signal path at a predetermined one of the at least three predesignated frequencies within the bandwidth of the stimulus signal, and solving for the frequency response (Gk) of the receiver using a first equation X1k=GkIIk and a second equation X2k=GkHk+1, wherein k is an integer that indexes the at least three predesignated frequencies.

20. The scheme of claim 12 further comprising determining a frequency response (Hk) of the signal path from the first combined frequency response (X1k) and the second combined frequency response (X2k) by designating one of the first frequency response of the signal path and the second frequency response of the signal path at a predetermined one of the at least three predesignated frequencies within the bandwidth of the stimulus signal, and solving for the frequency response (Gk) of the receiver using a first equation X1k=GkHk and a second equation X2k=GkHk+1, wherein k is an integer that indexes the at least three predesignated frequencies.