Digital Signal Processing Reference
In-Depth Information
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(a) Sample
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(b) Sample
Figure 2.13:
(a) The real part of a complex exponential series having 7.5 cycles per 73 samples; (b) The
imaginary part of a complex exponential series having 7.5 cycles per 73 samples.
F=3;N=240;
[seqCos,seqSin] = LVGenFreq(1.5ˆ(F/N),F,N)
The relationship given in Eq. (2.4) can be readily verified graphically and numerically using the
following script:
function LVPowerSeriesEquiv(M,k,N)
% LVPowerSeriesEquiv(0.9,3,64)
n = [0:1:N-1]; arg = 2*pi*k/N;
mags = (M.ˆn); maxmags = max(mags);
W2n = mags.*exp(j*arg).ˆn;
rightS = mags.*(cos(n*arg) + j*sin(n*arg));
figure(19); clf; hold on;
plot(real(W2n),imag(W2n),'bo');
plot(real(rightS),imag(rightS),'rx');
grid on; xlabel('Real'); ylabel('Imag')
axis([-maxmags,maxmags,-maxmags,maxmags])
