• 
  
• Design a 6th order Butterworth lowpass filter with a 200 Hz cutoff frequency at an 8000 Hz sample rate using MATLAB. See the sample MATLAB session on the course website. For the following designs, print out your matlab session, circling the final filter designs using:
  
  1. Impulse Invariance design
     ( Q1 )
  2. Bilinear design
     ( Q2 )
  3. Prewarped Bilinear design
     ( Q3 )
  (circle the numerator and denominator of H(z) for all three cases on your Matlab printout)

• On a separate sheet of paper, write out the transfer function H(z) for these three filters.( Q4 )
• Implement the Prewarped Bilinear design filter in the time domain (i.e., implement as in Fig. 6.3). Implement a new version of the "impulse response" button that plots the first 1024 points of the impulse response of this filter. (hint: write a function to apply an 1024-point long impulse as the input to your new filter function). ( P1 )
  
• Use the 20log|FFT| button to find the frequency response by taking the Fourier tranform of the foregoing time-domain impulse response and plot this ( P2 ), and estimate the cutoff frequency from the plot. ( Q5 )  (hint, to check your filter design, open disp.txt to find the 3dB point and its corresponding frequency in Hz.)
  
• Plot the spectrum of modint2.au. ( P3 )
  This is a QPSK modem at 1 KHz carrier frequency plus very strong interference from a DSB-SC signal and noise.
• Use the demodulator from the previous project to demodulate this signal.
  Plot the demodulated I channel output. ( P4 )
  Plot the spectrum of the demodulated I channel output. ( P5 )
  
• Use the demodulator from the previous project to demodulate this signal, but replace the filters with the Prewarped Bilinear design.
  Plot the new demodulated I channel output. ( P6 )
  Plot the FFT of the new demodulated I channel output. ( P7 )
  
<>Observe the different degrees of filtering evident in the frequency spectra of the I channel output using the moving average compared to using the Butterworth filter. How many dB down fom the dc signal peak of P5 is the DSB-SC interference signal of P5 for  the moving average filter? ( Q6 )  How many dB down fom the dc signal peak of P7 is the DSB-SC interference signal of P7 for the Prewarped Bilinear filter? ( Q7 )

Graduate students: see extra Project Presentation required below.

Turn in only the following code:

The following is required of all students registered in graduate level sections of the course.

Groups demonstrate a Bilinear filter design in lab, each group will be assigned a different filter design, in addition to the one called out in the project above. Depending on the number of demonstrations, a time limit of 10 minutes will be set. Time limits are strictly enforced. Grades will be determined by the quality of each demonstration including efficient use of time, clarity of presentation, completeness, and content. In such a short timeframe it is essential that you present only the most important details. All members of each group must participate in the demonstration. As a minimum, provide a printout showing filter coefficients, impulse response and frequency response. Also, include a Matlab simulation of the freq response. Demonstrations will be sometime during the last week of class; have your DSPsoundv55a program running with your filter design loaded, and be prepared to show the impulse response and frequency response.

Projects: