Quantization of wavelet transforms: use the signal generated in Experiment 10.1 and compute its \(N\)-stage wavelet transform with both the bior 4.4 and the \(\mathrm{db} 4\) wavelets. Use \(N=3, N=6\), and \(N=8\). Quantize its coefficients using several quantization step sizes \(q\). Use for the quantized value of \(\mathrm{x}\) the function \(q^{*}\) round \((x / q)\). Then reconstruct the signal from the quantized lowpass band and detail bands and observe the result. Repeat this exercise for the signal leleccum used in Experiment 10.2.

Transcribed Image Text:

Experiment 10.1 Here, we see how wavelets can be used to analyze nonstationary signals. We start by generating a signal composed of a sequence of five sinusoids of different frequencies, corrupted by spikes. The beginning of each sinusoid is specified in the pos_sin variable and the corresponding period is defined in T_sin. For the spikes, their amplitude and time positions are as given by the amp_imp and pos_imp variables respectively. The MATLAB code to generate it is as follows: N = 2000; t = [0:N]; x = zeros (size (t)); pos sin [0 600 1080 1380 1680 2000]; T_sin [100 40 20 10 5]; for i 1:5, m1+pos_sin(i); n = pos_sin (i+1); x(m:n) = end; sin(2*pi*t (1:n-m+1)/T_sin(i)); amp_imp = [3 2 2 2.5 -2.5]; pos imp [200 372 1324 1343 1802]; Timp [5 25 5 5 5 ]; for i 1:5, m 1 + pos_imp (i); n = 1 + pos_imp (i)+fix (T_imp (i)/2); x (m:n) = x (m:n) amp_imp (i) *sin(2*pi*t (1:n-m+1)/T_imp (i)). ^2; end;