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Unformatted text preview: Joshua Dean Lab 10: Octave Band Filtering April 25, 2011 The George Washington University School of Engineering and Applied Science ECE 3220 Digital Signal Processing Lab Section 30 GTA: Damon Conover Total Grade = 90 /100  Plot the frequency responses of Hamming BPFs with L=21,41,81 (10 points)  Show table of magnitudes and phases (L=21) (10 points)  Determine the passbands of the BPFs (10 points)  Determine the output signal when the given signal is filtered with a L=41 BPF (10 points)  BPF table containing upper, lower, and middle frequencies for each octave (10 points)  Determine the L require for each BPF filter (10 points)  Plot the frequency responses for the five scaled bandpass filters (10 points)  Section 5.3: Test the design, plot the outputs of the five BPFs (10 points)  Create octave scoring function (10 points)  Test the overall system and comment on results (10 points) Introduction The main goal of this lab was to create bandpass filters in attempt to extract information from sinusoidal signals. In the case of this lab, the signals were piano notes. Several bandpass FIR filters were designed and implemented in MATLAB. The filtered outputs were used in order to figure out which note was being played. The lab manual notes that there are 88 keys on a piano, but the requirements were to only have the octave of the note to be figured out by the designed filters. The firfilt() and conv() commands were used to implement the filters, while the freqz() command was called in order to obtain the filters frequency response. The result of this experiment is a better understanding of how to characterize a filter by knowing how it reacts to differing frequency components of the input. Lab Exercises Bandpass Filter Design Simple Bandpass Filter Design The L-point averaging filter is a lowpass filter with a passband width controlled by L. The passband width is inversely proportional to L. The lab manual notes that it is also possible to create a filter whose passband is centered on a nonzero frequency. The impulse response of the L-point FIR filter is defined as follows: Equation - Bandpass Filter Design L is the filter length, and c is the center frequency that defines the frequency location of the center of the passband. The first experiment required the generating of a bandpass filter that passed a frequency component at =0.4. The filter length was made to be equal to 40. The next section goes on to relate the passband of the BPF filter to be designed by the region of the frequency response where the transfer is close to its maximum value of one. The passband is defined as the length of the frequency region where the transfer function is greater than equivalently 0.707. The plot from the previous section above was used for the length-40 bandpass filter to determine the passband width using the 0. Level defining the passband....
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