Abstract:
A phase noise extraction apparatus and technique that extracts phase noise induced by a component of a transmitter from a radio frequency (RF) signal and attenuates noise induced from other sources. The RF signal is digitized, modulation is removed, and the carrier is suppressed to provide a noise signal including the phase noise and the noise induced from the other sources. A complementary autocorrelation operation is applied to the noise signal to attenuate the noise from the other sources. The correlated signal is transformed into the frequency domain to generate a power spectrum of the phase noise that may be measured or displayed.

Description:
BACKGROUND 
     Existing phase noise measurement techniques typically provide an aggregate measurement of so-called pure phase noise and phase noise from other sources induced on a radio frequency (RF) signal. The pure phase noise may be induced by components of a transmitter, such as an oscillator for example. The phase noise from other sources may originate from complex valued noise sources, and may include thermal noise, or various kinds of modulation-induced and synchronization-induced noise signals which may originate from a transmission filter, a non-ideal IQ modulator or timing uncertainty. It has been commonly accepted in the industry that pure phase noise and other phase noise induced on an RF signal can not be distinguished from each other, and generally can not be measured individually. 
     In the field of telecommunications, there is a need to measure phase noise induced by transmitters on complex digitally modulated signals such as wideband code division multiple access (WCDMA) and orthogonal frequency-division multiplexing (OFDM) signals including wireless local area network (LAN) signals and long term evolution (LIE) signals, as a way of testing the transmitters. However, such phase noise from the various other sources may mask the pure phase noise that is of interest for measurement. Existing phase noise measurement techniques typically do not have the ability to separately and accurately measure pure phase noise induced on RE signals. 
     There is therefore a need to provide improved phase noise extraction apparatuses and techniques that can distinguish between various types of phase noise and provide accurate measurement of pure phase noise. 
     SUMMARY 
     In a representative embodiment, a method includes digitizing a radio frequency (RF) signal that includes phase noise and secondary noise; removing, modulation and suppressing a carrier represented in the digitized signal to provide a composite noise signal including the phase noise and the secondary noise; applying a complementary autocorrelation on the composite noise signal to attenuate the secondary noise and provide a correlated noise signal substantially without the secondary noise; and representing a power spectrum of the phase noise responsive to the correlated noise signal. 
     In a farther representative embodiment, an apparatus includes a converter configured to digitize a radio frequency (RF) signal that includes phase noise and secondary noise; a processing unit configured to remove modulation and suppress a carrier represented in the digitized signal to provide a composite noise signal including the phase noise and the secondary noise; a correlator configured to apply a complementary autocorrelation on the composite noise signal to attenuate the secondary noise and to provide a correlated noise signal substantially without the secondary noise; and a generator configured to represent a power spectrum of the phase noise responsive to the correlated noise signal. 
     In a further representative embodiment, a non-transitory computer readable medium that stores a program executable by a computer for extracting phase noise from a radio frequency (RF) signal, the computer readable medium including a first code segment for digitizing the RF signal that includes the phase noise and secondary noise; a second code segment for removing modulation and suppressing a carrier represented in the digitized signal to provide a composite noise signal including the phase noise and the secondary noise; a third code segment for applying a complementary autocorrelation on the composite noise signal to attenuate the secondary noise and provide a composite noise signal substantially without the secondary noise; and a fourth code segment for representing a power spectrum of the phase noise responsive to the correlated noise signal. 
     In a further representative embodiment, an apparatus includes a converter configured to digitize a first radio frequency (RF) signal and a second RF signal that both include phase noise and secondary noise; a processing unit configured to remove modulation and suppress carriers represented in the first and second digitized signals to respectively provide a first composite noise signal and a second composite noise signal both including the phase noise and the secondary noise; a correlator configured to apply a complementary cross-correlation on the first and second composite noise signals to attenuated the secondary noise and provide a correlated noise signal substantially without the secondary noise; and a generator configured to represent a power spectrum of the phase noise responsive to the correlated noise signal. 
     In a still further representative embodiment, a method includes digitizing a radio frequency (RF) that includes amplitude noise and secondary noise; removing modulation and suppressing a carrier represented in the digitized signal to provide a composite noise signal including the amplitude noise and the secondary noise; applying a complementary autocorrelation on the composite noise signal to attenuate the secondary noise and provide a correlated noise signal substantially without the secondary noise; and representing a power spectrum of the amplitude noise responsive to the correlated noise signal. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The illustrative embodiments are best understood from the following detailed description when read with the accompanying drawing figures. Wherever applicable and practical, like reference numerals refer to like elements. 
         FIG. 1  is a block diagram illustrating a phase noise extractor  10 , according to a representative embodiment. 
         FIG. 2  is a block diagram illustrating a modulation remover  110 , according to a representative embodiment. 
         FIG. 3  is a graph illustrating phase noise power spectrum P(ω) extracted from an RF signal according to a representative embodiment, and a phase noise power spectrum including phase noise and noise from other sources. 
         FIG. 4  is a block diagram illustrating a phase noise extractor  30 , according to a representative embodiment. 
         FIG. 5  is a functional block diagram illustrating a computer system  500 , for executing an algorithm to control operations of phase noise extractor  10  of  FIG. 1 , according to a representative embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     In the following detailed description, for purposes of explanation and not limitation, illustrative embodiments disclosing specific details are set forth in order to provide a thorough understanding of embodiments according to the present teachings. However, it will be apparent to one having had the benefit of the present disclosure that, other embodiments according to the present teachings that depart from the specific details disclosed herein remain within the scope of the appended claims. Moreover, descriptions of well-known devices and methods may be omitted so as not to obscure the description of the example embodiments. Such methods and devices are within the scope of the present teachings. 
     Generally, it is understood that as used in the specification and appended claims, the terms “a”, “an” and “the” include both singular and plural referents, unless the context clearly dictates otherwise. Thus, for example, “a device” includes one device and plural devices. 
     As used in the specification and appended claims, and in addition to their ordinary meanings, the terms “substantial” or “substantially” mean to within acceptable limits or degree. For example, “substantially cancelled” means that one skilled in the art would consider the cancellation to be acceptable. As a further example, “substantially removed” means that one skilled in the art would consider the removal to be acceptable. 
     As used in the specification and the appended claims and in addition to its ordinary meaning, the term “approximately” means to within an acceptable limit or amount to one having ordinary skill in the art. For example, “approximately the same” means that one of ordinary skill in the art would consider the items being compared to be the same. 
       FIG. 1  is a block diagram illustrating a phase noise extractor  10 , according to a representative embodiment. In  FIG. 1 , phase noise extractor  10  receives a radio frequency (RF) signal from transmitter  20 . Transmitter  20  may include various transmitter components such as oscillator  210 , and may transmit any of various digitally modulated signals such as wideband code division multiple access (WCDMA) and orthogonal frequency-division multiplexing (OFDM) signals including wireless local area network (LAN) signals and long term evolution (LTE) signals. The RF signal may be transmitted from transmitter  20  without modulation. Phase noise extractor  10  may be a component of a receiver (not shown) such as a radio, mobile telephone, etc., or a component of an analyzer or a tester. The RF signal may include phase noise induced by a component  210  of transmitter  20 , and secondary noise induced by a source or sources other than component  210 . In this representative embodiment, component  210  of transmitter  20  is an oscillator, and may hereinafter be referred to as oscillator  210 . The phase noise may also be induced at transmitter  20  by instability of the time base, phase jitter in clock pulses of digital-to-analog converters and or phase-lock loops. The secondary noise may be characterized as complex-valued noise, and may be induced at transmitter  20 , induced at the receiver (not shown) or induced during transmission. The secondary noise may include thermal noise, additive spurious signals, or modulation-induced noise. The secondary noise induced on the RF signal at transmitter  20  may be caused by a non-ideal passband response of an intermediate frequency stage such as a non-flat amplitude response and/or a non-linear phase response, finite impulse response (FIR) filter truncation, IQ gain imbalance, IQ quadrature skew and IQ origin offset, for example. The secondary noise induced at the receiver may include synchronization-induced noise, which may be caused by timing misalignment for example. 
     As shown in  FIG. 1 , the RF signal from transmitter  20  is applied to down-converter  102 , which down-converts the RF signal in frequency to baseband or to an intermediate frequency sufficient for an analog-to-digital converter (ADC). The baseband or IF signal from down-converter  102  is applied to analog-to-digital converter (ADC)  104 , which samples the baseband signal to provide a discrete-time sequence (digitized signal) x(n). If the RF signal from transmitter  20  is modulated, switch  106  is switched to connect the digitized signal x(n) output from ADC  104  to modulation remover  110 . Modulation remover  110  removes the modulation from the carrier of digitized signal x(n) and suppresses the carrier, to provide a composite noise signal y(n), the composite noise signal y(n) including the phase noise and the secondary noise. 
       FIG. 2  is a block diagram illustrating modulation remover  110  according to a representative embodiment. As shown in  FIG. 2 , modulation remover  110  may include synchronizer  111 , demodulator  113 , modulation removal unit  115 , reference signal generator  117  and carrier suppressor  119 . Synchronizer  111  synchronizes digitized signal x(n) with the internal timebase in terms of carrier frequency and decision timing to enable coherent processing, and produces synchronized signal x(n), which is the synchronized version of digitized signal x(n). In addition, depending on the type of modulation on digitized signal x(n), further processing may be performed, such as unscrambling, matched filtering, channel equalization, extraction of useful parts of the signal, and estimation/compensation of multipath fading channels and/or IQ impairments. Demodulator  113  demodulates the synchronized signal x sync (n) to recover information bits. Reference signal generator  117  constructs the reference signal r(n), which is the ideal version of digitized signal x(n), by remodulating the information bits. Responsive to reference signal r(n) provided by reference signal generator  117 , modulation removal unit  115  removes the modulation from the synchronized signal x sync (n) to provide a carrier signal z(n) including the phase noise and the secondary noise, without the modulation. In an embodiment, modulation removal unit  115  divides synchronized signal x sync (n) by reference signal r(n) to provide carrier signal z(n) including the phase noise and the secondary noise, without modulation. Carrier suppressor  119  subsequently suppresses the carrier from the output of modulation removal unit  115  to provide composite noise signal y(n) including the phase noise and the secondary noise. 
     In an embodiment, synchronization may be achieved by synchronizer  111  of modulation remover  110  by utilizing known parts of digitized signal x(n), such as a pilot, preamble, midamble, or training sequence, depending on the specific format of digitized signal x(n). Alternatively, synchronization may be achieved by blind synchronization techniques that do not depend on such known signal parts. If digitized signal x(n) consists of only known parts, demodulator  113  of modulation remover  110  may be excluded. For improved synchronization performance, some of the blocks within modulation remover  110  may be repeated. For example, since reference signal r(n) can be considered as a known part of digitized signal x(n), a second synchronizer that is responsive to reference signal r(n) may be included to improve synchronization performance. With the modulation removed and the carrier suppressed, composite noise signal y(n) as output from modulation remover  110  includes substantially only the phase noise induced by oscillator  210  and the secondary noise. If the RF signal from transmitter  20  is not modulated, switch  106  is switched to connect digitized signal x(n) output from ADC  104  to carrier tracker  108 . Carrier tracker  108  tracks and suppresses the carrier of digitized signal x(n), to provide composite noise signal y(n) which includes substantially only the phase noise induced by oscillator  210  and the secondary noise. The aforementioned synchronization-induced noise previously identified as an example of the secondary noise may be induced during removal of the modulation and/or suppression of the carrier by modulation remover  110  and carrier tracker  108 . Modulation remover  110  and carrier tracker  108  may collectively be characterized as a processing unit. 
     As an example, in the case where the secondary noise induced from other sources consists only of thermal noise, digitized signal x(n) may be represented as
 
 x ( n )= s ( n ) e   jθ(n)   +v ( n )  (1),
 
where s(n) is a zero-mean, randomly-modulated baseband signal for the modulated signal case and s(n)=1 for the unmodulated ease, θ(n) is pure phase noise (real-valued), v(n) is thermal noise (complex-valued), j=√{square root over (−1)} and e is the base of the natural logarithm. Under the reasonable assumption that |θ(n)| sufficiently small, composite noise signal y(n) for n for which s(n)≠0 may be represented as
 
 y ( n )= x ( n )/ s ( n )−1 ≃j θ( n )+ v ′( n )  (2),
 
where v′(n)=v(n)/s(n) is an altered secondary noise signal which may be referred to as the secondary noise
 
     Switch  112  as shown in  FIG. 1  may be switched to provide composite noise signal y(n) from modulation remover  110  to correlator  114  when the RF signal is modulated, and to provide composite noise signal y(n) from carrier tracker  108  to correlator  114  when the RF signal is not modulated. Correlator  114  performs complementary autocorrelation on composite noise signal y(n). The complementary autocorrelation as applied on composite noise signal y(n) may be defined as
 
 c   y ( k )= E[y ( n ) y ( n−k )]  (3),
 
wherein E[·] represents the mathematical expectation and k is a time lag variable between respective samples of composite noise signal y(n). As a consequence of the statistical properties of the complementary autocorrelation, the secondary noise is attenuated or suppressed, so that correlated noise signal c y (k) output from correlator  114  substantially retains or includes only the phase noise induced by oscillator  210  in transmitter  20  substantially without the secondary noise. Of note, the mathematical expectation E[·] may not be computed in finite time. Therefore, for a sequence u(n) with length (n=1, . . . , N), the mathematical expectation may be approximated as E[u(n)]≃(1/N)Σ n=1   n u(n).
 
     As further shown in  FIG. 1 , correlated noise signal c y (k) from correlator  114  is output to frequency transformer (generator)  116 , which transforms correlated noise signal c y (k) to the frequency domain, to provide a power spectrum P(ω) of phase noise induced on the RF signal by oscillator  210  of transmitter  20 , substantially without the secondary noise. In a representative embodiment, frequency transformer  116  may be a Fourier transformer. In another representative embodiment, frequency transformer  116  may be a discrete Fourier transformer or a discrete-time Fourier transformer. The power spectrum P(ω) of phase noise may be subsequently measured, and/or output to a display (not shown) or provided as a printed hard copy to enable visualization of the phase noise induced by oscillator  210 . 
     As described, phase noise extractor  10  may be disposed as a component of a receiver such as a radio, mobile telephone, etc., or a component of an analyzer or a tester. The various “parts” of phase noise extractor  10  shown in  FIG. 1  may be physically implemented using a software-controlled microprocessor, hard-wired logic circuits, or a combination thereof. Although shown separately, the various “parts” may be implemented together. 
       FIG. 3  is a graph illustrating power spectrum P(ω) of phase noise extracted from an RF signal according to a representative embodiment (lower trace  900 ), and a phase noise power spectrum including phase noise and secondary noise from other sources (upper trace  910 ). Traces  900  and  910  were obtained from numerical simulation based on a synthetically generated Gaussian modulated signal x(n) with artificial phase noise and IQ impairments such as IQ gain imbalance, quadrature skew, and origin offset for example; linear distortion; and additive white Gaussian noise (AWGN). Trace  910  as shown includes the power spectrum of the phase noise induced by oscillator  210  of transmitter  20  described with respect to  FIG. 1 , in addition to the secondary noise. In contrast, trace  900  as shown includes the power spectrum of the phase noise induced by oscillator  210  of transmitter  20  described with respect to  FIG. 1 , substantially without the secondary noise.  FIG. 3  demonstrates how the phase noise induced by oscillator  210  of transmitter  20 , which typically would remain buried under noise introduced by a non-ideal IQ modulator having non-zero IQ imbalances, may be uncovered according to the representative embodiment described above. Of note, the rightmost portion of trace  900  includes remnants of complex-valued secondary noise that may be suppressed or attenuated more substantially as the number of signal samples of digitized signal x(n) is increased. The same attenuation effects have been verified on other kinds of secondary noise including but not limited to nonideal filtering, timing misalignment of digitally modulated signals, additive spurious signals, and additive colored noise. Incidentally, in trace  900  the complementary autocorrelation of complex-valued noise has larger peak-to-average ratio (PAR) than the PAR of the composite noise signal y(n) prior to autocorrelation. 
       FIG. 4  is a block diagram illustrating a phase noise extractor  30 , according to a representative embodiment. Phase noise extractor  30  may include similar features as phase noise extractor  10  shown in  FIG. 1 , including somewhat similar references numerals. Detailed description of such similar features may be omitted from the following. 
     In  FIG. 4 , phase noise extractor  30  receives a first radio frequency (RF) signal and a second RF signal from transmitter  20 . The first and second RF signals are nearly identical, and are received by phase noise extractor at substantially the same time. Transmitter  20  may include various transmitter components such as oscillator  210 , and may transmit the first and second RF signals as any of various digitally modulated signals such as WCDMA, OFDM, wireless LAN and LTE. The first and second RF signals may be transmitted from transmitter  20  without modulation. Phase noise extractor  30  may be a component of a receiver (not shown) such as a radio, mobile telephone, etc., or a component of an analyzer or a tester. The first and second RF signals may include phase noise induced by a component of transmitter  20  such as oscillator  210 , and secondary noise induced from other sources, similarly as described with respect to  FIG. 1 . In this representative embodiment, component  210  of transmitter  20  is an oscillator, and may hereinafter be referred to as oscillator  210 . 
     As shown in  FIG. 4 , the first and second RF signals from transmitter  20  are respectively applied to down-converters  302  and  322 , which down-convert the first and second RF signals in frequency to baseband or to an intermediate frequency sufficient for an ADC. The baseband or IF signals from down-converters  302  and  322  are respectively applied to ADCs  304  and  324 , which sample the baseband or IF signals to provide respective discrete-time sequences (first and second digitized signals) x 1 (n) and x 2 (n). If the first and second RF signals from transmitter  20  are modulated, switch  306  is switched to connect first digitized signal x 1 (n) output from ADC  304  to modulation remover  310  and switch  326  may be switched to connect second digitized signal x 2 (n) output from ADC  324  to modulation remover  330 . Modulation removers  310  and  330  remove the modulation from the carriers of first and second digitized signals x 1 (n) and x 2 (n) and suppress the carriers, to respectively provide first and second composite noise signals y 1 (n) and y 2 (n). With the modulation removed and the carrier suppressed, first and second composite noise signals y 1 (n) and y 2 (n) as output from modulation removers  310  and  330  include substantially only the phase noise induced by oscillator  210  and the secondary noise. If the first and second RF signals from transmitter  20  are not modulated, switch  306  is switched to connect first digitized signal x(n) output from ADC  304  to carrier tracker  308 , and switch  326  is switched to connect second digitized signal x 2 (n) output from ADC  324  to carrier tracker  328 . Carrier trackers  308  and  328  track and suppress the carriers of first and second digitized signal x 1 (n) and x 2 (n), to respectively provide first and second composite noise signals y 1 (n) and y 2 (n) which include substantially only the phase noise induced by oscillator  210  and the secondary noise. The aforementioned synchronization-induced noise previously identified as an example of secondary noise may be induced during removal of the modulation and/or suppression of the carrier by modulation removers  310  and  330  and carrier trackers  308  and  328 . Modulation removers  310  and  330  and carrier trackers  308  and  328  may collectively be characterized as a processing unit. 
     Switch  312  as shown in  FIG. 4  may be switched to provide the first composite noise signal y 1 (n) from modulation remover  310  to correlator  314  when the first RF signal is modulated, and to provide first composite noise signal y 1 (n) from carrier tracker  308  to correlator  314  when the first RF signal is not modulated. In a similar manner, switch  332  may be switched to provide second composite noise signal y 2 (n) from modulation remover  330  to correlator  314  when the second RF signal is modulated, and to provide second composite noise signal y 2 (n) from carrier tracker  328  to correlator  314  when the second RF signal is not modulated. 
     Correlator  314  performs a complementary cross-correlation operation on noise signals y 1 (n) and y 2 (n). The complementary cross-correlation operation as applied on first and second composite noise signals y 1 (n) and y 2 (n) may be defined as
 
 c   y12 ( k )= E[y   1 ( n ) y   2 ( n−k )]  (4),
 
wherein E[·] represents the mathematical expectation. As a consequence of the statistical properties of the complementary cross-correlation operation, the secondary noise is attenuated or suppressed, so that the correlated noise signal c y12 (k) output from correlator  314  becomes identical to correlated noise signal c y (k) of equation (3), and thus substantially retains or includes only the phase noise induced by oscillator  210  in transmitter  20  substantially without the secondary noise. In this embodiment, the complementary cross-correlation operation performed by correlator  314  is limited as performed on pairs of first and second composite noise signals y 1 ( n ) and y 2 ( n ) provided responsive to first and second RE signals that are both respectively modulated, or both respectively non-modulated.
 
     As further shown in  FIG. 4 , correlated noise signal c y12 (k) from correlator  314 , which is equal to correlated noise signal c y (k) as noted above, is output to frequency transformer (generator)  316 , which transforms correlated noise signal c y12 (k) to the frequency domain and provides a power spectrum. P(ω) of phase noise induced on the first and second RF signals by oscillator  210  of transmitter  20 , substantially without the secondary noise. The power spectrum P(ω) of phase noise may be subsequently measured, and/or output to a display (not shown) or provided as a printed hard copy to enable visualization of the phase noise induced by oscillator  210 . The two-path scheme of this embodiment as described with respect to  FIG. 4  enables separation of the phase noise induced by oscillator  210  that commonly exists in both the first and second RF signals, from other noise that independently exists in the first and second RF signals, such as phase jitter of ADCs  304  and  324  and pure phase noise of local oscillators in down-converters  302  and  322 . 
     In a similar manner as described with respect to  FIG. 1 , phase noise extractor  30  shown in  FIG. 4  may be disposed as a component of a receiver such as a radio, mobile telephone, etc., or a component of an analyzer or a tester. The various “parts” of phase noise extractor  30  shown in  FIG. 4  may be physically implemented using a software-controlled microprocessor, hard-wired logic circuits, or a combination thereof. Although shown separately, the various “parts” may be implemented together. 
       FIG. 5  is a functional block diagram illustrating a computer system  500 , for executing an algorithm to control operations of phase noise extractor  10  of  FIG. 1 , according to a representative embodiment. The computer system  500  may be any type of computer processing device, such as a PC, capable of executing the various steps of the programming language translation process. In various embodiments, the computer system  500  may be included in a receiver, an analyzer or a tester, and/or a separate controller or other processing device (not shown), or may be distributed among one or more of these devices. 
     In the depicted representative embodiment, the computer system  500  includes central processing unit (CPU)  571 , memory  572 , bus  579  and interfaces  575 - 577 . Memory  572  includes at least nonvolatile read only memory (ROM)  573  and volatile random access memory (RAM)  574 , although it is understood that memory  572  may be implemented as any number, type and combination of ROM and RAM and of internal and external memory. Memory  572  may provide look-up tables and/or other relational functionality. In various embodiments, the memory  572  may include any number, type and combination of tangible, non-transitory computer readable storage media, such as a disk drive, compact disc (e.g., CD-R/CD/RW), electrically programmable read-only memory (EPROM), electrically erasable and programmable read only memory (EEPROM), digital video disc (DVD), universal serial bus (USB) drive, diskette, floppy disk, and the like. Further, the memory  572  may store program instructions and results of calculations performed by CPU  571 . 
     The CPU  571  is configured to execute one or more software algorithms, including control of phase noise extractor  10  according to various embodiments described herein, e.g., in conjunction with memory  572 . The CPU  571  may include its own memory (e.g., nonvolatile memory) for storing executable software code that allows it to perform the various functions. Alternatively, the executable code may be stored in designated memory locations within memory  572 . The CPU  571  may execute an operating system, such as Windows® operating systems available from Microsoft Corporation or Unix operating systems (e.g., Solaris™ available from Sun Microsystems, Inc.), and the like. 
     In a representative embodiment, a user and/or other computers may interact with the computer system  500  using input device(s)  585  through I/O interface  575 . The input device(s)  585  may include any type of input device, for example, a keyboard, a track ball, a mouse, a touch pad or touch-sensitive display, and the like. Also, information may be displayed by the computer system  500  on display  586  through display interface  576 , which may include any type of graphical user interface (GUI), for example. 
     The computer system  500  may also include a control interface  577  for communicating with various components of phase noise extractor  10  shown in  FIG. 1 . For example, in various embodiments, the computer system  500  may communicate via a wired or wireless LAN, for example, as indicated by network  587 , and may control switches  106  and  112 , the sampling rate of ADC  104 , and frequency transformer  116 . Computer system  500  may control selection of modulation format, data capture length, start timing triggering, RF frequency and IF bandwidth filtering. The control interface  577  may include, for example, a transceiver (not shown), including a receiver and a transmitter, that communicates wirelessly over a data network through an antenna system (not shown), according to appropriate standard protocols. However, it is understood that the control interface  577  may include any type of interface, without departing from the scope of the present teachings. 
     In a representative embodiment, computer system  500  may carry out the functionality of phase noise extractor  10 . Computer system  500  may thus be configured to carry out all or part of the functionality of phase noise extractor  10  using program instructions which may be stored as code segment in any number, type and combination of the above noted tangible computer readable storage media or non-transitory computer readable medium. Phase noise extractor  10  may thus be virtually implemented. 
     The various “parts” shown in the computer system  500  may be physically implemented using a software-controlled microprocessor, hard-wired logic circuits, or a combination thereof. Also, while the parts are functionally segregated in the computer system  500  for explanation purposes, they may be combined variously in any physical implementation. In a farther representative embodiment, computer system  500  may be configured somewhat similarly as described above for executing an algorithm to control operation of phase noise extractor  30  shown in  FIG. 4 . 
     In a still further representative embodiment, either of phase noise extractors  10  and  30  may be used to respectively provide a power spectrum of amplitude noise induced by a component of transmitter  20 , such as oscillator  210 . Under conditions that the RF signal received from transmitter  20  is dominated by amplitude noise instead of phase noise at all offset frequencies of interest, phase noise extractors  10  and  30  extract amplitude noise. Consequently, the correlated noise signal c y (k) is dominated by amplitude noise, whereby frequency transformers  116  and  316  obtain the power spectrum of the amplitude noise as P(ω). 
     While specific embodiments are disclosed herein, many variations are possible, which remain within the concept and scope of the present teachings. Such variations would be apparent in view of the specification, drawings and claims herein. For example, in an embodiment baseband signals may be input to phase noise extractors  10  and  30  of  FIGS. 1 and 4  instead of RF signals. In such an embodiment, down-converters  102 ,  302  and  322  may be omitted from phase noise extractors  10  and  30 , in a further embodiment, discrete-time inputs may be provided as input to phase noise extractors  10  and  30  of  FIGS. 1 and 4  instead of RF signals. In such a further embodiment, down-converters  102 ,  302  and  322  and A/D converters (ADCs)  104 ,  304  and  324  may be omitted from phase noise extractors  10  and  30 . Also, if the total power of pure phase noise is all that is to be measured, frequency transformers  116  and  316  may be omitted from phase noise extractors  10  and  30 .