ELEN90058 - Signal Processing - Real-World Signal - Signal Processing Assignment Help

Assignment Task

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1. You are testing an algorithm you wrote. You must simulate sampling a real-world signal. You decide to use x(t) = cos(2πf1t) + 3 cos(2πf2t) as the mock real-world signal, where f1 is 10 kHz and f2 is 12 kHz.

The sampling rate is 48 kHz.
(a) Write the Matlab code for generating a sampled block of length 1024. Start at t = 0.
(b) Write the C code for generating a sampled block of length 2048. Start at t = 0.
2. This question concerns basic properties of filters.
(a) What do FIR and IIR stand for?
(b) Is y[k] = x[k − 1] + x[k] + x[k + 1] FIR or IIR?
(c) Is y[k] = x[k − 1] + x[k] + x[k + 1] causal?
(d) Is y[k] = x[k − 1] + x[k] + x[k + 1] stable?
(e) Is y[k] = 0.5y[k − 1] + x[k] FIR or IIR?
(f) Is y[k] = 0.5y[k − 1] + x[k] causal?
(g) Is y[k] = 0.5y[k − 1] + x[k] stable?

3. A 12 kHz real-valued sinusoid is sampled at 20 kHz.
(a) What is the definition of a frequency component of a continuous-time signal?
(b) What is the definition of a frequency component of a discrete-time signal?
(c) What frequency components are present in the original sinusoid?
(d) What frequency components are present in the sampled version?

4. A signal x(t) passes through a system whose impulse response h(t) has a single spectral null. The output of the system is observed.
(a) Write down the equation for the output y(t) in terms of the input x(t) and impulse response h(t).
(b) Can x(t) always be recovered perfectly from y(t)?

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