ELEC4620 Assessment Answers Digital Signal Processing

Filter used to denoise an ECG signal with muscle noise:

y[n]=1/21 (-2x[n]+3x[n-1]+6x[n-2]+7x[n-3]+6x[n-4]+3x[n-5]-2x[n-6])

This type of a filter will produce accurate results as we know that muscles in the human body expand and contract.This is rectified using this filter as it is giving weights to the averaging of the signal and they follow a oscillating pattern.This filter is of a linear nature

Recursive filter:

Kalman filter is a very popular filter in the family of recursive filters.These type of filters comprises of the prediction step and it updates the parameters by comparing with the actual output.This filter looks only at the previous steps output and the current step to reduce the noise.

Recursive filter proposed

y[n]=1/21 (-2x[n]+3x[n-1]+6x[n-2]+7x[n-3]+6x[n-4]+3x[n-5]-2x[n-6])+0.5*y(n-5)+0.9*y(n-4)

Signal

y=sin(0.35x)

Spectrogram of a signal

A spectrogram plots the signal strength at various frequencies of the waveform.

A spectrogram is generated by dividing the signal into various time quantas.And then the fast fourier transform is applied on the signal.The total number of divisions of the signal is known as the Frame count.Minimum and maximum frequency can also be specified.We can also specify the total number of fourier trasnforms taken.

FFT of a signal

F(s)= ∫_-∞^+∞f(x)e^-j2ỻxdx

If the total number of fourier transforms are less the spectrogram will have large gaps.

The spectrogram of a signal can be used to detect vibration.The vibration produced during the ignition of engine in car to the car reaching its destination will have a very identical spectrogram but in a defective car the spectrogram will be different.

Spectrogram of the Mainstreet wav file:

Frequency range =0 to 1500

The sample rate of the signal is 16000 hz

Duration is 12.009 seconds

Screenshot of properties of signal analysed with audio test bench

To evaluate the quality of compression of two codecs we can plot the PSNR to the bit rate and this is known as the rate distortion curve.We know that the higher values of PSNR to the compared signal is a good measure of quality of the compression.The BD metric provides us with a single metric to compare the quality of the two signals.

Signals=

HEVC_MOS=[42.5,44.8,46,47.1]

bitrate=[1,1.1,1.2,1.3,1.4,1.5,1.6,1.8,3,6]

bitrate1=[2.1,2.2,2.3,2.4,2.5,2.6,2.7,3.7,7.5,8.1]

HEVC_PSNR=[42.5,42.7,42.9,43.1,43.2,43.3,43.5,44.8,46,47.1]

AVC_MOS=[2,5.1,8.2]

AVC_PSNR=[38.1,38.3,38.4,38.5,38.8,38.9,41,41.2,43.8,45.2]

Dh[PSNR]=46.6066

Dl[PSNR]=46.4904

Function from matlab exchange

Bd metric=-0.1107

References:

1. Serge (2022). Bjontegaard metric calculation (BD-PSNR) (https://www.mathworks.com/matlabcentral/fileexchange/41749-bjontegaard-metric-calculation-bd-psnr), MATLAB Central File Exchange. Retrieved January 25, 2022.