Resampling a signal without using built-in command

Attached below is my effort of doing this question but I was not able to obtain required output:

clear; clc;

f = 30;

fs = 200;

t = 0:(1/fs):1;

x = cos(2*pi*f*t);

figure;

stem(0:200,x(1:201),'LineWidth',1)

title('Orignal Signal')

%%%%%%%%%%%%%%%%%%% Part A %%%%%%%%%%%%%%%%%%

R_a = 1.66;

[L_a,M_a] = rat(R_a);

t_a_i = 0:((1/fs)/L_a):1/L_a;

x_a = cos(2*pi*f*t_a_i);

figure;

subplot(2,1,1)

stem(0:200,x_a(1:201),'LineWidth',1)

title('Signal Is Interpolated')

t_a_ii = 0:((1/fs)*M_a):1*M_a;

y_a = (x_a.*t_a_ii);

subplot(2,1,2)

stem(0:200,y_a(1:201),LineWidth=1)

title('Signal Is Then Decimated')

sgtitle('Signal is resampled by Interpolation & then Decimation')

Kindly guide me in this.

Answer 1

[AndresVar]

Regarding t: Your time intervals don't need to change length just the step size.

Regarding x_a: you need to keep only the samples from the orignal signal other samples should be zero

Regarding y_a: you can just use colon indexing to downsample ever other 'M_a' smaples

Also, typically you need to do low pass filtering. When you interpolate first upsample then low pass using the fs_original/2. When you decimate, low pass first with fs_final/2.

To get your new signals you can use loops or some built in indexing methods

[N,D]=rat(1.66)
t_original = 0:1/fs:1
t_interpol = 0:1/fs/N:1;
t_decimate = t_interpol(1:D:end) % OR 0:1/fs/N*D:1, note you downsample the upsampled signal

x_original = % evaluate at t_original
x_interpol = % you can evaluate at t_interpol, BUT you should only keep the samples at times in t_original
x_decimate = x_interpol(1:D:end) % look at x_interpol and keep samples at times t_decimate

% for x_interpol and x_decimate you can use loops, or check out
doc ismember % to see when t_interpol and t_original are the same ex. x2(~ismember(t2,t))=0
doc intersect % similar use to ismember ex. [~,idx] = intersect(t2,t)

% i recommend you compare your results to the built in methods
doc upsample
doc downsample
doc resample % note resample has special filter to remove artifacts