Question

I wrote a Matlab program for the figure below. When I plot the waves, they look the same. Why do the two waves frequencies look same and How do I avoid it? (I really do need this part of the question answered.)

N = 200; % Total number of time domain samples in simulation.

Fs = 100 ;% sampling frequency.

F1 = 10; % frequency of wave - 1.

F2 = 90; % frequency of wave - 2.

phi = 0; % zero phase signal.

t=0:(1/Fs):(N-1)/Fs; % time samples.

y1 =sin(2*pi*F1*t+phi); %first sinwave.

y2= sin(2*pi*F2*t+phi); %second sinwave

% plotting above functions in continuous and discrete time.

subplot 221; plot(t, y1); xlabel('Time in sec F1 = 10Hz'); ylabel('Amplitude'); grid on;

subplot 222; plot(t, y2); xlabel('Time in sec F2 = 90 hz'); ylabel('Amplitude'); grid on;

Answer 1

Original output by your code:

Why both waveform look same even frequency of both signal is different:

- we are sampling a sine wave signal with frequency of 100Hz.

- Frequency of first sine wave is 10Hz and as per Nyquist formula sampling frequency must be greater than equal to 2 time of highest frequency( fs >= 2*f). This condition is satisfied for first sine wave.

- In case of second sine wave, highest frequency is 90Hz and according to above formula sampling frequency must be greater than equal to 2*90 = 180Hz. But in this case it is not satisfied sampling frequency is 100Hz instead of 180Hz.

update code : Fs = 200 ;% sampling frequency.

- In above picture we can see both waveform is having different frequency. We have divided plot window in 2x2 part and we are using only first 2 part.

-We can divide into 2 part only in vertical part.

update code:

subplot (2,1,1); plot(t, y1); xlabel('Time in sec F1 = 10Hz'); ylabel('Amplitude'); grid on;

subplot (2,1,2); plot(t, y2); xlabel('Time in sec F2 = 90 hz'); ylabel('Amplitude'); grid on;

- As we are having very low sampling rate for high frequency sine wave. Due to that in above diagram you can see second sine wave is having different magnitude.

- To avoid this we can increase sampling frequency further

update code: Fs = 1000 ;% sampling frequency.

matlab code:

%//////////////////////////////////////////////////////////////////////////

N = 200; % Total number of time domain samples in simulation.
Fs = 1000 ;% sampling frequency.
F1 = 10; % frequency of wave - 1.
F2 = 90; % frequency of wave - 2.
phi = 0; % zero phase signal.
t=0:(1/Fs):(N-1)/Fs; % time samples.
y1 =sin(2*pi*F1*t+phi); %first sinwave.
y2= sin(2*pi*F2*t+phi); %second sinwave
% plotting above functions in continuous and discrete time.
subplot (2,1,1); plot(t, y1); xlabel('Time in sec F1 = 10Hz'); ylabel('Amplitude'); grid on;
subplot (2,1,2); plot(t, y2); xlabel('Time in sec F2 = 90 hz'); ylabel('Amplitude'); grid on;

%//////////////////////////////////////////////////////////////////////////

- code which I have changed is in BOLD TEXT