The spectrum of a real-time signal y(t), which is bandlimited to 20 kHz, is to be...
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The spectrum of a real-time signal y(t), which is bandlimited to 20 kHz, is to be inspected using a 1024-point FFT (Fast Fourier transform) of the discrete-time sequence y(n) = y.(nT), where T' is the sampling period. Determine an appropriate range of sampling frequencies Fs(min) ≤ 1/T ≤ Fs(max), such that aliasing is avoided, and then compute the spacing in Hz between the resulting frequency bins when Fs(min) is used. Assume the time taken to compute one 1024-point FFT is 0.6 ms. (8 Marks) b) Draw a signal flow diagram for a 4-point radix-2 DIT FFT, labelling all the input and output nodes and marking the values of all twiddle factors, and then use the diagram to compute the DFT of the sequence {4, 2, 2, 4). (8 Marks) c) You are designing and building a real-time spectrum analyser, which provides the spectra of digitised analogue signals using a 2048-point radix-2, DIT FFT. The DSP processor used in the analyser is capable of performing one addition in 1 clock cycle and one multiplication in 4 clock cycles. Estimate the maximum sampling frequency the system can support if the clock frequency of the processor is 1.2 GHz. Ignore all other computation overheads. (9 Marks) The spectrum of a real-time signal y(t), which is bandlimited to 20 kHz, is to be inspected using a 1024-point FFT (Fast Fourier transform) of the discrete-time sequence y(n) = y.(nT), where T' is the sampling period. Determine an appropriate range of sampling frequencies Fs(min) ≤ 1/T ≤ Fs(max), such that aliasing is avoided, and then compute the spacing in Hz between the resulting frequency bins when Fs(min) is used. Assume the time taken to compute one 1024-point FFT is 0.6 ms. (8 Marks) b) Draw a signal flow diagram for a 4-point radix-2 DIT FFT, labelling all the input and output nodes and marking the values of all twiddle factors, and then use the diagram to compute the DFT of the sequence {4, 2, 2, 4). (8 Marks) c) You are designing and building a real-time spectrum analyser, which provides the spectra of digitised analogue signals using a 2048-point radix-2, DIT FFT. The DSP processor used in the analyser is capable of performing one addition in 1 clock cycle and one multiplication in 4 clock cycles. Estimate the maximum sampling frequency the system can support if the clock frequency of the processor is 1.2 GHz. Ignore all other computation overheads. (9 Marks)
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