I am trying to FM modulate a signal but the frequency of the modulated wave remains constant. We are not allowed to use fmmod or cumsum functions, only int() or quad() functions are allowed.
% Generation of FM
clc
clearvars
sampling_freq = 1000; % fs = 1Khz
time = 0:(1/sampling_freq):0.1;
syms t
message = 0.2*cos(2*pi*10*t); % m(t) = Am*sin(2*pi*fm*t)
carrier = 1*sin(2*pi*200*t); % c(t) = Ac*sin(2*pi*fc*t)
modulator_sensitivity = 50; % Modulator sensitivity
integrated(t) = int(message, t);
modulated = 1*cos(2*pi*200*t + 2*pi*modulator_sensitivity*integrated)
beta = (modulator_sensitivity * 0.2) / 10; % beta = (kf*Am)/fm
fplot(modulated, [time(1) time(end)])
title("Message and Modulated Signal")
hold on
fplot(message, [time(1) time(end)])
Plotted message and modulated waves
Related
The amplitude of a FFT should be depending on the length of the signal.
To display the result in a independent way the Power Spectral Density or the Amplitude Spectral Density should be used. There are calculated as follows:
Amplitude FFT = Y
Signal Length = L
Power Spectral Density PSD = Y^2/L
Amplitude Spectral Density ASD = Y/sqrt(L)
https://www.sjsu.edu/people/burford.furman/docs/me120/FFT_tutorial_NI.pdf
My problem is, that the result of the Matlab fft is already indipendent from the signal length and I do not understand if this is already a PSD or a ASD.
Let's take the Matlab example Noisy Signal: https://ch.mathworks.com/help/matlab/ref/fft.html
If we make the FFT on the same signal, but twice or ten times longer, the FFT amplitude does not change.
This because of the line:
P2 = abs(Y/L);
where the amplitude is divided through the signal length. But why is the formula different from the PSD or the ASD formula and we still obtain amplitudes indipendent from the signal length?
In this example it is shown, that the two signals, ones for 50s, ones for 500s, has almost the same amplitudes.
% Signal 1
sps = 1000; % Sampling frequency
T = 1/sps; % Sampling period
Frequency1 = 150; % frequency 1 [Hz]
SignalAmplitude1 = 1; % mm/s
Frequency2 = 45; % dominant frequency [Hz]
SignalAmplitude2 = 1.2; % mm/s
L = 50; % Length of signal, sek.
L = L*1000; % convert to ms
time = (0:L-1)*T; % Time vector
Signal = cos(2*pi*Frequency1*time)*SignalAmplitude1 + sin(2*pi*Frequency2*time)*SignalAmplitude2;
f = sps*(0:(L/2))/L;
FFTcomplex = fft(Signal);
P2 = abs(FFTcomplex)/L;
P1 = P2(:,round(1:L/2+1));
P1(:,2:end-1) = 2*P1(:,2:end-1);
Ampl_FFT_1 = P1;
% Signal 2
sps = 1000; % Sampling frequency
T = 1/sps; % Sampling period
Frequency1 = 150; % frequency 1 [Hz]
SignalAmplitude1 = 1; % mm/s
Frequency2 = 45; % dominant frequency [Hz]
SignalAmplitude2 = 1.2; % mm/s
L = 500; % Length of signal, sek.
L = L*1000; % convert to ms
time = (0:L-1)*T; % Time vector
Signal = cos(2*pi*Frequency1*time)*SignalAmplitude1 + sin(2*pi*Frequency2*time)*SignalAmplitude2;
f = sps*(0:(L/2))/L;
FFTcomplex = fft(Signal);
P2 = abs(FFTcomplex)/L;
P1 = P2(:,round(1:L/2+1));
P1(:,2:end-1) = 2*P1(:,2:end-1);
Ampl_FFT_2 = P1;
sum(Ampl_FFT_2)-sum(Ampl_FFT_1)
I am trying to make an acoustic modem with matlab. It records sound an stores it in an array, modulates it using 64-QAM and adds then demodulates it. But the demodulated sound and recorded sound are not the same.
Here is the code:
clear;
clc;
M = 64; % Modulation order (alphabet size or number of points in signal constellation)
k = log2(M);
Fs=44100;
Nbits=8;
nChannels=1;
SNR=250;
%audio recording
recObj=audiorecorder(Fs,Nbits,nChannels);
recDuration=3;
disp("Begin speaking.")s
recordblocking(recObj,recDuration);
disp("2 sec pause")
pause(2)
disp("End of recording")
y=getaudiodata(recObj);
plot(y);
% playObj=audioplayer(y,Fs);
% play(playObj);
Ts=-(1/Fs)/2:1:(1/Fs)/2;
figure
subplot(1,2,1);
plottf(y,Ts,'t');
subplot(1,2,2);
plottf(y,Ts,'f');
%MODULATION QAM
y_int = abs(round(y*1000/16));
constdiag = comm.ConstellationDiagram('XLimits',[-sqrt(M) sqrt(M)],'YLimits',[-sqrt(M) sqrt(M)]);
qamData = qammod(y_int,M);
constdiag(qamData)
%DEMODULATION QAM
demodData = qamdemod(noisySound,M);
demodData = demodData*16/1000;
isequal(y_int,demodData);
playObjn=audioplayer(demodData,Fs);
play(playObjn);
%LOWPASS FILTER
Fn = Fs/2; % Nyquist Frequency (Hz)
Wp = 1000/Fn; % Passband Frequency (Normalised)
Ws = 1010/Fn; % Stopband Frequency (Normalised)
Rp = 1; % Passband Ripple (dB)
Rs = 150; % Stopband Ripple (dB)
[n,Ws] = cheb2ord(Wp,Ws,Rp,Rs); % Filter Order
[z,p,k] = cheby2(n,Rs,Ws,'low'); % Filter Design
[soslp,glp] = zp2sos(z,p,k); % Convert To Second-Order-Section For Stability
figure(3)
freqz(soslp, 2^16, Fs) % Filter Bode Plot
filtered_sound = filtfilt(soslp, glp, demodData);
%sound(filtered_sound, 44100)
where am i doing wrong?
I tried 16QAM and 32QAM but result is the same.
I have a half wave sin:
Rc = 1e2; % [b/s] chip rate
T =1; % [s/b] inverse of chip rate
Fs = 2e2; % [Hz] sampling frequency
dt = 1/Fs; % [s]
sps = 40;
dt2=dt/sps;
T = 1;
% single pulse time reference
t = 0:dt2:2*T;
pulse_half_Sine = sin(pi*t/(2*T)).^3;
I have a modulated signal
N=1e4;
bits=randi([0,1],N,1);
modOrder = 2;
modData = pammod(bits,modOrder);
I want to do a convolution of the signal and the pulse. The duration of the envelope is T and the symbolic speed = 2/T. Thus, the maximum should be at the point T/2. I do so, but I don't get the countdown points of time.
over_data=upsample(modData,length(pulse_half_Sine)-1);
plot(t, pulse_half_Sine);
signal1 = conv(over_data,pulse_half_Sine);
I'm making a bandpass filter and I've created a signal with some unwanted frequencies based on sinusoids:
Fs = 8e3; % Sampling Rate
fn = Fs/2; % Nyquist frequency
L = 1e3; % Length of signal
T = 1/Fs; % Sampling period
t = T*linspace(0,L,Fs); % Time domain
% Frequencies in Hz
f1 = 1500;
f2 = 700;
f3 = 2500;
f4 = 3500;
% Signal
x = 6*sin(2*pi*f1*t);
% Noise
noise = 3*sin(2*pi*f2*t)...
+ 2*sin(2*pi*f3*t)...
+ 1*sin(2*pi*f4*t);
x_noise = x + noise;
I then create a Butterworth bandpass filter:
[b,a] = butter(10,[1000 2000]/fn,'bandpass');
The signal in time and frequency space, with the bandpass response (with freqz) looks like this:
Fig. 1 Signal with corruption | Fig. 2 Frequency with bandpass response
I would've figured from here on, simply doing
xf = filter(b,a,x_noise);
would've yielded something very similar to the original signal, but alas, what I get is really far from the filtered signal with a high response far from the bandpass.
What am I doing wrong here?
Here's the full code:
clear all
Fs = 8e3; % Sampling Rate
fn = Fs/2; % Nyquist frequency
L = 1e3; % Length of signal
T = 1/Fs; % Sampling period
t = T*linspace(0,L,Fs); % Time domain
% Frequencies in Hz
f1 = 1500;
f2 = 700;
f3 = 2500;
f4 = 3500;
% Signal
x = 6*sin(2*pi*f1*t);
% Noise
noise = 3*sin(2*pi*f2*t)...
+ 2*sin(2*pi*f3*t)...
+ 1*sin(2*pi*f4*t);
x_noise = x + noise;
subplot(221);
idx = 1:round(length(t)/30);
plot(t(idx),x(idx),t(idx),x_noise(idx));
xlabel('Time (s)'); ylabel('Signal Amplitudes');
legend('Original signal','Noisy signal');
% Frequency space
f = fn*linspace(0,1,L/2+1);
X = fft(x_noise)/L;
[b,a] = butter(10,[1000 2000]/fn,'bandpass');
h = abs(freqz(b,a,floor(L/2+1)));
subplot(222);
plot(f,abs(X(1:L/2+1)),f,h*max(abs(X)));
xlabel('Freq (Hz)'); ylabel('Frequency amplitudes');
legend('Fourier Transform of signal','Filter amplitude response');
% Filtered signal
xf = filter(b,a,x_noise);
subplot(223)
plot(t(idx),xf(idx));
xlabel('Time (s)'); ylabel('Signal Amplitudes');
legend('Filtered signal');
% Filtered in frequency space
Xf = abs(fft(xf)/L);
subplot(224);
plot(f,Xf(1:L/2+1),f,h*5e-6);
xlabel('Freq (Hz)'); ylabel('Frequency amplitudes');
legend('Fourier Transform of filtered signal','Bandpass');
Your time variable t is wrong, e.g 1/(t(2)-t(1)) should give Fs but it doesn't.
Try instead:
t = T*(0:L-1);
I am little bit confused with fft. That would be good if anyone can help me. first, I want to convert fft output in time domain. Where t = f/k and K = BW/Tm (BW = bandwidth & Tm = transmit time). After that again i need to take fft and ouput should be box (rectangular function) which is having width of BW(40e9).
f1 = 1e6; % first cutoff frequency
f2 = 4e6; % second cutoff frequency
BW = 40e9; % bandwidth
Tm = 0.2e-3; % transmit time
fs = 1e7; % sampling frequency
c = 3e8; % speed of light
w1 = f1/ (fs/2); % normalizing first cutoff frequency
w2 = f2/ (fs/2): % normalizing second cutoff frequency
[b,a] = butter(2, [w1,w2], 'bandpass');
load('fb2040');
x = fb2040(3,:);
y_filt = filter(b,a,x); % filtering
nfft = length(y_filt);
res = fft(y_filt, nfft)/ nfft;
f = fs/2 * linspace(0,1,nfft/2+1);
res = res(1:nfft/2+1);
figure, plot(f,abs(res));
xlabel('frequency in MHz');
ylabel('amp');
return