Week 7

David B. And Mohamed A.

1) What is the effect of the pulse width on the experiment? 
Try settings like 0.1, 1.0, and 10 msec. Report your observations in your documentation.

The length of the pulse determines how many frequencies it needs to reproduce it. Shorter lengths
(as t->0) the pulse becomes more like a delta function which contains all frequencies, while longer lengths
do not include all frequencies (at least not with equal weights as the delta function). The tube acting as a
transfer function picks out all the possible harmonics of the pulse which correspond to the properties 
of the tube. Shorter pulses contain more frequencies therefore more harmonics are shown on the FFT, while longer pulses lack much of the high frequency harmonics.

2)What is the effect of the acquisition rate? Try settings like 1000, 10000 and 100000 points per sec.
 Also note what the minimum buffer size and scan rate is needed to describe the response up to 2000 Hz.

The acquisition rate sets the top limit of the FFT, this being due to the Niquist frequency (a signal of frequency f must be sampled at a rate of at least 2*f to prevent aliasing). Thus the FFT response is limited in its range to half of the sampling frequency. For example to measure a response up to 2000Hz one needs at least a 4000Hz sampling rate. Additionally, the buffer size must be long enough to capture the signal until it decays to zero,to collect the entire response.

3)Try the effect of signal averaging on the appearance of the power spectrum. For this experiment, reduce the gain of the audio amplifier until the signal is barely detectable.

By averaging multiple trials we are able to improve our signal-to-noise ratio. This is due to the central limit 
Theorem which states that the mean deviation improves by the inverse sqrt of N(trials). So the more trial are averaged,the deviation decreases, which is very beneficial to defeat unwanted noise from weak signals.