The DFT - Synthesis Lectures on Signal Processing - page 181

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Frequency, Hz

Figure 3.56: DFT (positive frequencies only) of the entire test audio signal, comprised of the audio file
'drwatsonSR8K.wav', normalized to maximum unity magnitude, to which has been added a sine wave of
amplitude 0.008 and frequency of 1000 Hz.

% LVxZxformFromSamps([1,1,1,1],[1],6,5000,10)
% LVxZxformFromSamps([1],[1,0,0.64],36,5000,100)
Theoretically, x

1. Obviously,
however, many IIR impulse responses decay away to a magnitude of essentially zero in a finite number of
samples, so provided that the number of z -transform samples obtained is large enough, reconstruction of
X(z) can be performed to a reasonable approximation. This is demonstrated by the second test call given
above, the result of which is shown in Fig. 3.62.
31. Evaluate the DTFT of the original sequence, sinc-interpolated sequence, and linear-interpolated
sequence created by the script LVxInterp8Kto11025 , which was developed in Volume I of the series, for
the chapter on sampling and binary representation. For the interpolated sequences, evaluate the DTFT
both before and after the post-interpolation lowpass filtering. For each evaluation, use 1024 signal
samples, perform a DFT of length 2ˆ15, and plot the positive frequency response only in decibels, with
the maximum response for each plot being zero dB. Figures 3.63 and 3.64 show the plots that should be
created, for example, in response to the call

[ n ] must be finite length, i.e., identically zero for n< 0 and n ≥ N −

LVxInterp8Kto11025(0,2950)

32. Write the m-code for the following function specification, the purpose of which is to verify the
correctness of Eq. (3.34) in the text. Test your script with the given test calls.
function LVxIDF TviaPosK(TestSig)
% Test signal must be real