The output of an electronic device is a (real-valued) digital signal at a sample rate of 25 kHz. lts frequency content,

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The Output Of An Electronic Device Is A Real Valued Digital Signal At A Sample Rate Of 25 Khz Lts Frequency Content 1 (320.08 KiB) Viewed 38 times

The output of an electronic device is a (real-valued) digital signal at a sample rate of 25 kHz. lts frequency content, when interpreted as a continuous-time signal, is guaranteed to lie between 4kHz and 8kHz. You must design a system that takes this digital signal as an input and upsamples it, to make its sample rate 75kHz. (a) (2 points) Draw a diagram indicating clearly where the frequency content of the digital signal lies. Include negative frequencies. Label the diagram using normalised frequency. (Do not use Matlab's definition of normalised frequency.) (b) (1 point) To upsample the signal, you will first add N zeros betwecn cach sample. What value of N will you use? (c) (2 points) Draw a diagram indicating clearly how the frequency content of this signal relates to that of the original signal. (d) (5 points) To complete the upsampling operation, you will next apply a filter. You wish to use an FIR filter, and prefer a shorter filter to a longer one. Write down the pass band regions, where you want your signal to be passed unaltered. Also write down the stop band regions, where you want your filter to heavily attenuate the signal. Fully justify your answer. You need only consider non-negative frequencies. (e) (2 points) Given the pass band and stop band regions, you could in principle ask Matlab to design an FIR filter for you. Alternatively, you could simply use a low-pass filter, as taught in lectures. What is the disadvantage of using a low-pass filter in this application? (f) (3 points) One way to make an FIR low-pass filer is by truncating the impulse response of an ideal low-pass filter. Why is this normally a bad way of making a low-pass filter? What is a simple way of modifying this filter to improve its performance? Why does this lead to an improvement?