Questions tagged [autocorrelation]
Autocorrelation is the cross-correlation of a signal with itself.
501 questions
3
votes
2
answers
356
views
Auto/Cross-correlation of a sinusoidal signal
If we do auto-correlation or even cross-correlation of a sinusoidal signal, I can see multiple peaks, but they decay as the lag index increases, it looks like the output is divided by the lag index?. ...
- 455
0
votes
0
answers
41
views
Is my Autocorrelation Function up to Par?
I am using python to play around with my own implementation of the ACF. I am aware of how the autocorrelation function can have quantization error due to integer values of lag being used to calculate ...
0
votes
2
answers
72
views
Getting the impulse response of a linear system given white gaussian noise as input and the system's output
I am having trouble with my implementation:
...
- 101
1
vote
2
answers
123
views
Can a wide sense stationary, white noise process have variance?
A discrete time wide sense-stationary process is one where $ E(X[n]) = E(X[m]) $ for all n,m and $ E(X[n+m]X[n]) = E(X[m]X[m]) $). It is white noise if $E(X) = 0$ and E(X[n]X[n])=0 for $n \neq 0$. ...
1
vote
0
answers
50
views
How to compute the power spectral density of a vector-valued process without mirroring the autocorrelation function?
I'm simulating a 2D Ornstein-Uhlenbeck process (Langevin equation for velocity), and I'm interested in computing the power spectral density (PSD) of the vector-valued velocity process.
Following the ...
- 111
0
votes
1
answer
83
views
Implementing Antares Auto-Tune patent (US5973252A): missing details in autocorrelation-based pitch detection and low-latency correction
I tried implementing the autocorrelation as described in the patent to no luck. Is there something obvious they have left out? The patent has expired now, but there sure as hell isn't any plugin that ...
5
votes
0
answers
152
views
Kalman Filter with correlated measurement noise derivation
I have made great efforts on the derivation, and the results are really close but I am still missing the last step. If someone can help that'd be great!
Problem setup
Consider this modified Kalman ...
- 51
0
votes
1
answer
121
views
Questions about FFT Based GPS Acquisition
I am working on implementing GPS acquisition on an FPGA with an AD9361 RF front end. My approach involves:
Taking the ADC data and performing an FFT.
Taking the FFT of the PRN code (which remains ...
1
vote
1
answer
49
views
GPS L1 C/A Auto-Correlation IFFT weird peaks at the end
I am performing GPS autocorrelation on an FPGA. I generate C/A code 1 using MATLAB and upsample it to 4 × 1.023 Msps. This results in a total of 4092 samples, which I then zero-pad to 4096. After ...
- 11
0
votes
2
answers
87
views
Issues with Early-Late Discriminator in DS-CDMA Receiver
I am developing a receiver for a DS-CDMA signal modulated with QPSK. The I part of the signal is spread using one sequence, while the Q part is spread using a different sequence. The chip time is 16 ...
1
vote
1
answer
204
views
What is the average value of an autocorrelation function?
Given an autocorrelation function $R_{xx}(\tau)$ for a random process $x(t)$ the formulae to find its mean is generally given as $$\mu_x^2=\lim_{\tau\rightarrow\infty}R_{xx}(\tau)$$
but if the ...
- 109
1
vote
1
answer
141
views
DTFT of an autocorrelation function is producing a complex PSD?
I'm trying to find the PSD of a pretty simple autocorrelation function for a discrete random process, $R_x[k]=\cos(ω_0k)$.
From a data-book for Z-transforms, $g_k =\cos(ω_0k)$ transforms into $$G(z)=\...
- 13
1
vote
2
answers
64
views
Handling Summation in Autocorrelation Function for PAM Signals with Random Shifts
I am working on the autocorrelation function of a Pulse Amplitude Modulated (PAM) signal, which is given by:
$$
X(t)=\sum_{n=-\infty}^{\infty} A_n p(t-n T-\phi)
$$
where:
$A_n$ are i.i.d. random ...
- 35
1
vote
1
answer
148
views
A proof of Wiener–Khinchin theorem without change of variables
I wonder if the following proof of Wiener–Khinchin theorem (for stochastic signals) is wrong:
We'll be first proving the Wiener–Khinchin theorem for deterministic power signals, and then we will just ...
- 11
0
votes
0
answers
37
views
WSS process generation discrepancies using different methods
I want to produce a WSS process with a certain PSD that follows an AR characteristics. I am using MATLAB to code it. When I use the ARIMA function as follow
...
- 101