I'm trying to plot the equation shown in the image, but I'm not sure how to apply the Galois Seq. "gf()" here.
Can you please help me with this?
enter image description here
clear all
close all
clc
%%
Fs = 1000; % Sampling frequency
T = 1/Fs; % Sampling period
L = 1024; % Length of signal
t = 2*(0:L-1)*T; % Time vector
signal = 0;
m = 5;
for k=1:((2^m)-1)
g = gf(2^m);
signal = signal + g(k).*exp(1i*2*pi*k*t)/((2^m)-1);
end
figure
subplot(2,2,1)
plot(t,signal)
title('signal')
Related
I'm trying to plot the Gauss sums according to the equation shown in the image s(t), but I keep receiving errors.
Can you please show me what am I doing wrong ?
%%
Fs = 1000; % Sampling frequency
T = 1/Fs; % Sampling period
L = 1024; % Length of signal
t = 2*(0:L-1)*T; % Time vector
x = 0;
k = 0;
s = 0;
p = primes(L);
% s(t) = cumsum((k/p)(1:length(p)-1)).*exp(1i*k*t);
for k=1:p-1
s(t) = s(t) + (k/p).*exp(1i*k*t);
end
figure
subplot(2,2,1)
plot(t,s)
title('signal')
You're treating the Legendre symbol as fraction - which it is not despite the deceivingly similar appearance.
Furthermore the index for your summation doesn't make a whole lot of sense, you probably just wan to use s as summing variable. So you just have to replace k/p in your summation expression with the Legendre symbol.
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 have an OFDM signal which is giving me half the power spectrum (half the bandwidth) I am meant to have. I am been told the phase assignment is what is causing it but I have been twitching on it for days.... still not having the right answer
prp=1e-6;
fstep=1/prp;
M = 4; % QPSK signal constellation
k = log2(M); % bits per symbol
fs=4e9;
Ns=floor(prp*fs);
no_of_data_points = (Ns/2);
no_of_points=no_of_data_points;
no_of_ifft_points = (Ns); % 256 points for the FFT/IFFT
no_of_fft_points = (Ns);
nsamp = 1; % Oversampling rate
fl = 0.5e9;
fu = 1.5e9;
Nf=(fu-fl)/fstep;
phin=zeros(Nf,1);
dataIn = randint(no_of_data_points*k*2,1,2); % Generate vector of binary
data_source = randsrc(1, no_of_data_points*k*2, 0:M-1);
qpsk_modulated_data= modulate(modem.qammod(M),data_source);
modu_data= qpsk_modulated_data(:)/sqrt(2);
[theta, rho] = cart2pol(real(modu_data), imag(modu_data));
A=angle(modu_data);
theta=radtodeg(theta);
figure(3);
plot(modu_data,'o');%plot constellation without noise
axis([-2 2 -2 2]);
grid on;
xlabel('real'); ylabel('imag');
%% E:GENERTION
phin = zeros(Nf,1);
phin(1:Nf,1)=theta(1:Nf);
No = fl/fstep;
Vn = zeros(Ns,1);
for r = 1:Nf
Vn(r+No,1) = 1*phin(r,1);
% Vn(r+No,2) = 1*phin(r,2);
end
%%
%------------------------------------------------------
%E. Serial to parallel conversion
%------------------------------------------------------
par_data = reshape(Vn,2,no_of_data_points);
%%
% F. IFFT Transform each period's spectrum (represented by a row of
% time domain via IFFT
time_domain_matrix =ifft(par_data.',Ns);
You are only considering the real part of the signal.
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
Need help since kind of lost on this. I am trying to graph the code below i have in which I made a white noise and used STFT to do the bandpass filtering but now I need to graph the signal in to two graphs for each channel. The result should be graphs. For graph 1a., the horizontal axis should be frequency, the vertical axis should be amplitude. For (2).b, the horizontal axis should be time, the vertical axis should be frequency, and express the amplitude using color.
function newwhitenoise()
L = 5000; %Sample length for the random signal
Pause = 10000; %Sample Pause Gap
mu = 0;
sigma = 2;
%Need to see left signal is not displaying
Left_signal = sigma*randn(L,1) + mu;
Right_signal = sigma*randn(L,1) + mu;
Long_signal = [Left_signal zeros(L,1); zeros(Pause,2); zeros(L,1) Right_signal];
%Player Object
soundRecord(Long_signal);
disp([Left_signal zeros(L,1)]);
%sound(Long_signal, Fs);
%Plots subplots in graph
%figure
%subplot(211);
%plot(Left_signal, 'b'); grid on;
%subplot(212);
%plot(Right_signal, 'r'); grid on;
end
function signalplayer(signal)
%load(signal);
fs = 44100; %Sample Frequency
obj = audioplayer(signal,fs);
play(obj);
end
function soundRecord (signal)
fs = 44100; %Sample Frequency
recObj = audiorecorder(44100, 16, 2);
get(recObj)
%save sound to wave file
%filename = 'location.flac';
audiowrite('input.wav',signal, fs);
if ~exist('inFile')
inFile = 'input.wav';
end
if ~exist('outFile')
outFile = 'output.wav';
end
if ~exist('frameWidth')
frameWidth = 4096; % size of FFT frame, better be a power of 2
end
frameHop = frameWidth/2;
analWindow = hanning(frameWidth);
[inBuffer, Fs] = wavread(inFile);
x = [inBuffer(:,1); linspace(0, 0, frameWidth)']; % use left channel only, zeropad one frame at the end
clear inBuffer;
numSamples = length(x);
numFrames = floor(numSamples/frameHop)-1;
% disp(frameWidth);
% disp(numSamples);
% disp(frameHop);
% disp(numFrames);
% disp(size(analWindow));
% disp(size(transpose(analWindow)));
y = linspace(0, 0, numSamples)';
n = 0; % init sample pointer. unlike MATLAB, i like counting from 0
for frameIndex = 1:numFrames
xWindowed = x(n+1:n+frameWidth) .* analWindow; % get and window the input audio frame
X = fft(fftshift(xWindowed)); % do the FFT
Y = X; % copy the input spectrum to output
% do whatever processing to Y that you like
yWindowed = fftshift(real(ifft(Y))); % convert back to time domain, toss the imaginary part
%disp(size(x(1:frameWidth)));
%disp(size(yWindowed));
y(n+1:n+frameWidth) = y(n+1:n+frameWidth) + yWindowed;
n = n + frameHop;
end
wavwrite(y, Fs, 'output.wav');
For graph 1 try pwelch and for graph 2 try spectrogram.
pwelch is basically the average of the squared magnitude of the STFT. The spectrogram function returns the STFT of the signal thus it operates on the signal in the time domain.
Both functions are called with the same input parameters and when called with no output, plot the result on the current axes.
If you want the frequency axis to be the vertical (y) in graph 2, use the option 'yaxis' in the call for spectrogram. I suggest you look at the documentation of both functions.