Sampling Rate Conversion Notes

8/13/2019 Sampling Rate Conversion Notes

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Different Sampling Rates

can be applied for

transforming an analog signal

into a discrete one.

xc(t)

Sampling Frequency (Fs)

is the inverse

of sampling period ,i.e. Fs=1/Ts

x n = xc n s

x[n]= xc(n Ts),

Ts = 2 Ts

x[n]=xc(nTN)


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Our task is to change the sampling rate

of a given discrete-time signal

in a way that respects thesampling thorem


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Reducing the Sampling Rate by an integer factor

xd [n] = x [n M] = xc (n M Ts)

A sequence x[n] can be downsampled

In the same way that in the original discretization

tha sampling rate should obey

N

during the additional sampling step

Fs/ M > 2 FN

Hence, low-pass filtering is usually introduced

to prevent aliasing effects


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Increasing the Sampling Rate by an integer factor

xi[n] = xc (n Ts) , with s=s/L

Starting with a given sequence x[n] ,we can increase the rateby predicting intermediate signal values

The procedure includes the addition of zeros between samples

and the use of a low-pass filtering to smooth out the discotinuities


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Change Sampling Rate by rational factor

Using a system that increases the sampling rate

by a factor I,

in cascade sonnection with a system that reduces the rateb a factor D

we can achieve resampling by non-integer factor


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% plot the signal and scale the time-axis

size(signal); t=1:100000; time=t*(1/Fs);figure(1),subplot(2,1,1),plot(t,signal),xlabel('discrete-time')

subplot(2,1,2),plot(time,signal),xlabel('sec')

% Define Heart-Ratefigure(2),plot(time(1:20000),signal(1:20000))

[tt,dontcare]=ginput(2)

RRT=tt(2)-tt(1); HeartRate=1/RRT

>> HeartRate = 1.2635 Hz


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%%%%__________ A : Reducing Sampling Ratehelp downsample

signal1=signal(1:10000);

figure(3),subplot(3,1,1),plot(signal1)

signal2=downsample(signal1,3);subplot(3,1,2),plot(signal2)

signal3=downsample(signal1,30);subplot(3,1,3),plot(signal3)

% notice the clipping in the second beat


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%_____ Improvement using Decimate

signal4= decimate(signal1,40); plot(signal4)% Decimate includes filter for the aliasing problem


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%%%%_______ B : INCREASE Sampling Rate

signal5= upsample(signal1,2);

subplot(2,1,1),plot(signal1), subplot(2,1,2),plot(signal5)% NOTICE: zeros are inserted


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%_C: change the rate by a rational factor

signal7= resample (signal1,3,2);

subplot(2,1,1),plot(signal1),subplot(2,1,2),plot(signal7)


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% A demo on Filtering ECG-data

sgolaydemo

help ecg


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Digoxin Effect

The morphology of the QRS complex / ST segment is variouslydescribed as either slurred, sagging or scooped and resemblingeither a reverse tick, hockey stick or my personal favourite!

Salvador "ali#s moustache$

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Sampling Rate Conversion Notes