Matlab

1. Bulld/construct 95 order (96 coetficients in total) perflect reconstruction fiters with passband edges of the lowpass and highpass fiters of 0.45 and 0.55, respectively. HINT: You may want to investigate use of "lirpr2chfb". a. Plot the magnitude of the frequency response for each of the quadrature mirror fitters prior to normalizing. Describe your observations. b. Normalize the filters such that the gain is 17 atter undergoing both the analysis and synthesis phases of the QMF bank. Describe your observations. 2. Implement two-channel perfect reconstruction OMF bank (Page 817 of text and in Figure 1 below). The figure below is that of a 2-channel QMF bank. HINTS: 1) Make sure all filters used in the QMF bank are normalized (unity gain), and 2) You may consider using the polyphase form. NOTE: You have been provided both polyphase decimator and interpolator functions in class. Figure 1: Two-channel Quadrature Mirror Filker Bank Page 1 of 2 3. Perform the following for ANY 3 of the following input flies: ceramiccup mat. chirp mat, splatmat and mysterious mat: a. Produce the Welch PSD estimate for the input flie, x, b. Process the input fle and capture the oulput of the Quef Analysis stage. i. Playback the output for each of the QNF Analysis fisers and describe/discuss/state your observations. ii. Produce the Welch PSD estimate of the ouput for each of the OMF Analysis fiters and describe/discuss/state your obsenations. c. Continue the processing by capturing the output for each of the QMF Synthesis fillers. i. Playback the output for each of the ONF Syrthesis fitters prior to performing the signal addition/reconstruction and describeldiscuss/state your observations. ii. Produce the Weich PSD estimate for cutput for each of the QMF Synthesis fitters prior to reconstruction and descrbeldiscuss/state your observations. d. Produce the Weich PSD estimate for the reconstructed signal, f^. Describe/discuss/state your observations. e. Estimate the QMF system trans'er function and plot the estmated system transfer function in db. Describeidiscuss/state your observations. f. Compute the mean squared error and state your observations. i.e. MSE=i=1N(x(0)x(i))2/N Where x(i) is the input signal sequence and A(d) is the output reconstructed signal estimate after undergoing the perfect reconstruction QMF bank. 4. Summarize your overall observations based on the two-channel GMF bank processing of the input data. 1. Bulld/construct 95 order (96 coetficients in total) perflect reconstruction fiters with passband edges of the lowpass and highpass fiters of 0.45 and 0.55, respectively. HINT: You may want to investigate use of "lirpr2chfb". a. Plot the magnitude of the frequency response for each of the quadrature mirror fitters prior to normalizing. Describe your observations. b. Normalize the filters such that the gain is 17 atter undergoing both the analysis and synthesis phases of the QMF bank. Describe your observations. 2. Implement two-channel perfect reconstruction OMF bank (Page 817 of text and in Figure 1 below). The figure below is that of a 2-channel QMF bank. HINTS: 1) Make sure all filters used in the QMF bank are normalized (unity gain), and 2) You may consider using the polyphase form. NOTE: You have been provided both polyphase decimator and interpolator functions in class. Figure 1: Two-channel Quadrature Mirror Filker Bank Page 1 of 2 3. Perform the following for ANY 3 of the following input flies: ceramiccup mat. chirp mat, splatmat and mysterious mat: a. Produce the Welch PSD estimate for the input flie, x, b. Process the input fle and capture the oulput of the Quef Analysis stage. i. Playback the output for each of the QNF Analysis fisers and describe/discuss/state your observations. ii. Produce the Welch PSD estimate of the ouput for each of the OMF Analysis fiters and describe/discuss/state your obsenations. c. Continue the processing by capturing the output for each of the QMF Synthesis fillers. i. Playback the output for each of the ONF Syrthesis fitters prior to performing the signal addition/reconstruction and describeldiscuss/state your observations. ii. Produce the Weich PSD estimate for cutput for each of the QMF Synthesis fitters prior to reconstruction and descrbeldiscuss/state your observations. d. Produce the Weich PSD estimate for the reconstructed signal, f^. Describe/discuss/state your observations. e. Estimate the QMF system trans'er function and plot the estmated system transfer function in db. Describeidiscuss/state your observations. f. Compute the mean squared error and state your observations. i.e. MSE=i=1N(x(0)x(i))2/N Where x(i) is the input signal sequence and A(d) is the output reconstructed signal estimate after undergoing the perfect reconstruction QMF bank. 4. Summarize your overall observations based on the two-channel GMF bank processing of the input data