Question

An analog signal, bandlimited to 20 Hz is corrupted by high-frequency noise. The spectrum of the noise is from 25 Hz to 35 Hz. The noisy analog signal is sampled at 60 Hz. A digital lowpass filter is to be designed so as to remove the noise from the signal. Find the desired frequency response.

Answer 1

Given

fm=20Hz

fs= 60hz

by nyquist criteria

fs>= 2fm.......Above condition satisfies the nyquist criteria

Now at the detection side

we have combination of analog message signal +Nosie signal

and low pass filter is used to remove unwanted noise signal

just we have to use the RC Low pass filter which will remove high frequency noise from original signal

proper choice of RC

fc= 1/2*pi*RC....... cut off frequency

here cutt off frequency of 20Hz for low pass filter assume value of R or C and calculate other value

Now for frequency response, When we get cut off frequency fc our frequency response will be from 0Hz - 20 Hz

Noise Component gets removed from message signal i.e 25Hz-35-Hz we cant get any signal because our cut off frequency of LPF limited to 20Hz only.

and by considering gain magnitude Amax ,?the 3dB down magnitude(0.707Amax) gives fc i.e. cut off frequency

Frequency spetrum contain only fm message signal component.