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A digital filter has an input-output relationship expressed by the difference equation $$y(n)=\frac{x(n)+x(n-1)+x(n-2)+x(n-3)}{4}$$ .
The signal $x(n)$ equals $\delta (n)-\delta (n-1)$ .
A discrete-time, shift invariant, linear system produces an output $y(n)=\{1, -1, 0, 0, \dots \}$ when its input $x(n)$ equals a unit sample.
A discrete-time system has transfer function $H(e^{i\times 2\pi f})$ . A signal $x(n)$ is passed through this system to yield the signal $w(n)$ . The time-reversed signal $w(-n)$ is then passed through the system to yield the time-reversed output $y(-n)$ . What is the transfer function between $x(n)$ and $y(n)$ ?
The slang word “hum” represents power line waveforms that creep into signals because of poor circuitconstruction. Usually, the 60 Hz signal (and its harmonics) are added to the desired signal. What weseek are filters that can remove hum. In this problem, the signal and the accompanying hum have been sampled;we want to design a digital filter for hum removal.
Thinking that digital implementations are always better, our clever engineer wants to design a digital AM receiver. The receiverwould bandpass the received signal, pass the result through an A/D converter, perform all the demodulationwith digital signal processing systems, and end with a D/A converter to produce the analog message signal.Assume in this problem that the carrier frequency is always a large even multiple of the message signal's bandwidth $W$ .
A problem on Samantha's homework asks for the 8-point DFT of the discrete-time signal $\delta (n-1)+\delta (n-7)$ .
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