A DTMF decoding system needs two pieces: a bandpass filter to isolate individual frequency components, and...

 

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A DTMF decoding system needs two pieces: a bandpass filter to isolate individual frequency components, and a detector to determine whether or not a given component is present. The detector must "score" each possibility and determine which frequencies are most likely present. In a practical system where noise and interference are present, this scoring process is a crucial part of the system design, but we will only work with noise-free signals to understand the basic functionality in the decoding system. 4.1 Filter Design The filters that will be used in the filter bank (Fig. 2) are a simple type constructed with sinusoidal impulse responses. In the section on useful filters in Chapter 7, a simple bandpass filter design method was presented in which the impulse response of the filter is simply a finite-length cosine of the form: 2 2п fin Ax) = cos (25/ h[n] COS L 0<n<L where L is the filter length, and f, is the sample frequency. The parameter f, defines the frequency location of the passband, e.g., we pick fb = 697 if we want to isolate the 697 Hz component. The bandwidth of the bandpass filter is controlled by the larger the value of L, the narrower the bandwidth. (a) Generate a bandpass filter, h770, for the 770 Hz component with L = 64 and fs = 8000. Plot the filter coefficients in the first panel of a two-panel subplot using the stem () function. (b) Generate a bandpass filter, h1336, for the 1336 Hz component with L64 and fs = 8000. Plot the filter coefficients in the second panel of a two-panel subplot using the stem () function. (c) Use the following commands to plot the frequency response (magnitude) of h770 fs = 8000; ww = 0: (pi/256) :pi; % only need positive freqs ff = ww/(2*pi) *fs; H = freqz (h770, 1, ww); plot (ff, abs (H)); grid on; (d) Indicate the locations each of the DTMF frequencies (697, 770, 852, 941, 1209, 1336, and 1477 Hz) on the plot from part (c). Hint: use the hold and stem () commands. (e) Comment on the selectivity of the bandpass filter h770, i.e., use the frequency response to explain how the filter passes one component while rejecting the others. Is the filter's passband narrow enough? (f) Plot the magnitude response of the h1336 filter and compare its passband to that of the h770 filter. A DTMF decoding system needs two pieces: a bandpass filter to isolate individual frequency components, and a detector to determine whether or not a given component is present. The detector must "score" each possibility and determine which frequencies are most likely present. In a practical system where noise and interference are present, this scoring process is a crucial part of the system design, but we will only work with noise-free signals to understand the basic functionality in the decoding system. 4.1 Filter Design The filters that will be used in the filter bank (Fig. 2) are a simple type constructed with sinusoidal impulse responses. In the section on useful filters in Chapter 7, a simple bandpass filter design method was presented in which the impulse response of the filter is simply a finite-length cosine of the form: 2 2п fin Ax) = cos (25/ h[n] COS L 0<n<L where L is the filter length, and f, is the sample frequency. The parameter f, defines the frequency location of the passband, e.g., we pick fb = 697 if we want to isolate the 697 Hz component. The bandwidth of the bandpass filter is controlled by the larger the value of L, the narrower the bandwidth. (a) Generate a bandpass filter, h770, for the 770 Hz component with L = 64 and fs = 8000. Plot the filter coefficients in the first panel of a two-panel subplot using the stem () function. (b) Generate a bandpass filter, h1336, for the 1336 Hz component with L64 and fs = 8000. Plot the filter coefficients in the second panel of a two-panel subplot using the stem () function. (c) Use the following commands to plot the frequency response (magnitude) of h770 fs = 8000; ww = 0: (pi/256) :pi; % only need positive freqs ff = ww/(2*pi) *fs; H = freqz (h770, 1, ww); plot (ff, abs (H)); grid on; (d) Indicate the locations each of the DTMF frequencies (697, 770, 852, 941, 1209, 1336, and 1477 Hz) on the plot from part (c). Hint: use the hold and stem () commands. (e) Comment on the selectivity of the bandpass filter h770, i.e., use the frequency response to explain how the filter passes one component while rejecting the others. Is the filter's passband narrow enough? (f) Plot the magnitude response of the h1336 filter and compare its passband to that of the h770 filter.

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a Generate bandpass filter h770 Define the parameters Sample frequency fs 8000 Hz Filter length L 64 ... View the full answer