1. We wish to extract tones at 150 and 250 Hz from tones at 1050 and 1150 Hz and then downsample the output by the largest possible factor. Assume the signal containing the four tones is sampled at 40 kHz. Use a Kaiser window FIR filter with a passband from 0 to 300Hz (3 dB down at band edge) and attenuation > 80 dB at 500 Hz. Implement the filter, maximally downsample the output, and examine the output spectrum to ensure that it meets specifications. Now reimplement the filtering and downsampling with a single polyphase downsampling filter. Compare the number of operations required for the original FIR implementation and the polyphase implementation. (4 marks) 2. Upsample the output of the downsampling filter of Question 1 back to the original 40 kHz sampling rate by designing an appropriate upsampling filter using zero packing and low-pass filtering. Then reimplement as a polyphase upsampling filter. Check the output of the polyphase upsampler against the filtered zero-packed output to show they are the same. Compare the number of operations required for the original single-rate FIR implementation from Q1 and the polyphase downsampling/upsampling implementation in this question. (6 marks) 3. Without incurring additional computation, modify the polyphase upsampling filter to frequency shift the data by heterodyning with a 2.4 kHz carrier. That is the tones at 150, and 250 Hz will now be placed at 2150, 2250, 2550, and 2650 Hz. Document Preview:

ELEC4620/7462 Digital Signal Processing Assignment 3 (revised 10/09/19) (Due Date: Monday 16/09/2019 at 5pm) 1. We wish to extract tones at 150 and 250 Hz from tones at 1050 and 1150 Hz and then downsample the output by the largest possible factor. Assume the signal containing the four tones is sampled at 40 kHz. Use a Kaiser window FIR filter with a passband from 0 to 300Hz (3 dB down at band edge) and attenuation > 80 dB at 500 Hz. Implement the filter, maximally downsample the output, and examine the output spectrum to ensure that it meets specifications. Now reimplement the filtering and downsampling with a single polyphase downsampling filter. Compare the number of operations required for the original FIR implementation and the polyphase implementation. (4 marks) 2. Upsample the output of the downsampling filter of Question 1 back to the original 40 kHz sampling rate by designing an appropriate upsampling filter using zero packing and low-pass filtering. Then reimplement as a polyphase upsampling filter. Check the output of the polyphase upsampler against the filtered zero-packed output to show they are the same. Compare the number of operations required for the original single-rate FIR implementation from Q1 and the polyphase downsampling/upsampling implementation in this question. (6 marks) 3. Without incurring additional computation, modify the polyphase upsampling filter to frequency shift the data by heterodyning with a 2.4 kHz carrier. That is the tones at 150, and 250 Hz will now be placed at 2150, 2250, 2550, and 2650 Hz. (4 marks) Simulation Exercise Simulate the single rate system of Q1 in Simulink. Listen to the output on the loudspeaker/headphones. Shows graphs and images in your report. Method 1. Create new Simulink Model 2. Open Simulink Library Browser 3. Select Sine Wave Source 4. Set parameters as per Q1 5. Build model with Spectrum Analyser, Filter, and Scope 6. Ask Tutors for help?…

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