## Forums Search for: Autocorrelation

## estimation of autocorrelation matrix or eigenvalue spread.

inHi everyone, I am experimenting with some equalization schemes and to judge the performance, I need to estimate the eigenvalue spread of the...

Hi everyone, I am experimenting with some equalization schemes and to judge the performance, I need to estimate the eigenvalue spread of the input to the equalizer. Currently I am working with a single input stream of many thousands of samples, and I am assuming that my data is more or less uniformly distributed. To get the eigenvalues, I generate R = Sum( x[k]*x[k]T) where x[k] is a vector...

## Pitch recognition of a musical note on a smart phone

inHi. With limited resources such as slower CPUs, code size and RAM, how best to detect the pitch of a musical note, similar to what a tuner...

Hi. With limited resources such as slower CPUs, code size and RAM, how best to detect the pitch of a musical note, similar to what a tuner would do? Should I use: - Kiss FFT - FFTW - autocorrelation - zero crossing analysis - octave-spaced filters other? Thank you in advance. -mz

## Levinson algo. wtih complex coef. required

inHi, I am desperatly looking for a generalized Levinson algorithm that can cope with complex autocorrelation values and giving complex filter...

Hi, I am desperatly looking for a generalized Levinson algorithm that can cope with complex autocorrelation values and giving complex filter coefficients... I would like to implement it in C, and i have only found the classical LPC analysis but it can not deal with complex coefficients... Anyone can help ? Thanks in advance

## error caused by Wien-Hammerstein system (Bussgang?)

Hi, I have the following setup: x ---> [ G(z) ]-----> [ (.)^3 ]-----> [ H(z) ]-----> y where x is a Gaussian input with E(x)=0 and...

Hi, I have the following setup: x ---> [ G(z) ]-----> [ (.)^3 ]-----> [ H(z) ]-----> y where x is a Gaussian input with E(x)=0 and autocorrelation Rxx. For simplicity, I can set Rxx=sigma^2*delta(tau) and G(z)=1, i.e. a pure Hammerstein system driven with white Gaussian noise (I would like to generalize afterwards if possible): x ---> [ (.)^3 ]-----> [ H(z) ]-----> y Now I would lik

## Noise estimation

inHello, Is there a method to estimate the statistical properties of additive noise from a received signal observation. Assume we have y(k)...

Hello, Is there a method to estimate the statistical properties of additive noise from a received signal observation. Assume we have y(k) = x(k) + n(k) and we observe the received signal y(k). I would like to know if there is a way to determine the autocorrelation of the noise process n(k), that is Rnn. This is not a speech problem. x(k) is a digital PAM signal that is corrupted ...

## ARMA model statistical properties

inI have an ARMA process with known parameters. Are there general expressions for variance and possibly autocorrelation of the output for such...

I have an ARMA process with known parameters. Are there general expressions for variance and possibly autocorrelation of the output for such processes? I can find the above for an order-(1,1) process in for example Shanmugan & Breipohl's "Random Signals" (Wiley, 1988), but is it possible for higher orders? If it helps, I would be happy to confine the processess in question to order (p,p...

## Detection of frequency with minimum latency

inHi , Rune said in thread of "Basics of Spectral Density and Autocorrelation" that it is possible to detect a single sine wave in a data...

Hi , Rune said in thread of "Basics of Spectral Density and Autocorrelation" that it is possible to detect a single sine wave in a data stream. How to do it ? I have a low frequency time series data (7Hz to 50Hz) I need to get its sprectum with minimum latency. and with 1Hz resolution. What should I do ? Regards and thanks, Devidas

## Simple Question on Random Variables and Random Processes

inLet X(t) be a stationary white noise process with autocorrelation function R_{xx}(\tau) = N0 * \delta(\tau). Let V be a random...

Let X(t) be a stationary white noise process with autocorrelation function R_{xx}(\tau) = N0 * \delta(\tau). Let V be a random variable determined from X(t) by V = \int_{-\infty}^{+\infty} X(t) dt. How do you compute statistics on V, like E[V^2]? Yes, this is a homework problem. -- % Randy Yates % "Watching all the days go by... %% Fuquay-Varina, NC ...

## LPC using cumulants

inHi All, I want to implement LPC using cumulants (instead of LPC using autocorrelation ) algorithms in C. Where can I find that algorithms. some...

Hi All, I want to implement LPC using cumulants (instead of LPC using autocorrelation ) algorithms in C. Where can I find that algorithms. some formulas or c code.

## LMS maximum step size

inHi all, w(n+1) = w(n) + mu*e(n)*x(n) Can anyone tell me how to determine the maximum mu? I read some materials that mu should be less than...

Hi all, w(n+1) = w(n) + mu*e(n)*x(n) Can anyone tell me how to determine the maximum mu? I read some materials that mu should be less than 2/lambda_max, where lambda_max is the maximum eigen value of the autocorrelation matrix of the input. Take the 50Hz noise cancellation filter in Widrow's paper as an example, "Adaptive Noise Cancelling : Principles and Applications". How to determine t...

## GSM AMR optimization

inHi, I am optimizing GSM AMR reference code. The optimization needs not to be bit-exact, in fact, some quality degradation is permitted. I...

Hi, I am optimizing GSM AMR reference code. The optimization needs not to be bit-exact, in fact, some quality degradation is permitted. I have done all the obvious things like primitives inlining, autocorrelation approximation, etc. Are there any other mathematical shortcuts to make the codec faster? Right now, the codec is 25% slower that I need it to be. TIA, ~Yaroslav

## Scaling factor in inverse fourier transform

inHi all, I tried to calculate the autocorrelation from FFT using C. As far as I know the input for the inverse FT is the power spectrum density...

Hi all, I tried to calculate the autocorrelation from FFT using C. As far as I know the input for the inverse FT is the power spectrum density of the data X(t) PSD = (Xreal(f)^2 + Ximag(f)^2) / N, N is the length of the real number After calculating the inverse FT, I scaled the result with 1/N but the result is not 1 (less than 1). I wonder if I made mistake with the scaling factor or ...

## algorithms for location versus for frequency?

inI suppose all characterization of signals inside some buffer of samples is a form of statistical signal processing. When asking about the...

I suppose all characterization of signals inside some buffer of samples is a form of statistical signal processing. When asking about the frequency of some signal in comp.dsp, all sorts of algorithms are mentioned, forms of autocorrelation (or squared difference, etc.), or fft/dft usage (windowed, zero padded, phase differentiated, etc.). Also, there seem to be lots of textbooks on these ...

## Plot of Autocorrelation Error using LMS in Matlab

Hi !! I hope somebody can help !! N = 8000; % Number of Samples n = 0:N-1; sigmax = 0.01 L = 12 f1 = 101.7 f2 = 142.4 f3 =...

Hi !! I hope somebody can help !! N = 8000; % Number of Samples n = 0:N-1; sigmax = 0.01 L = 12 f1 = 101.7 f2 = 142.4 f3 = 231.5 fs = 1000 K = 20 % Number of realizations cumensq = zeros(K,N) en1 = zeros(K,N) % length of filter coefficients wn = zeros(1,L); a = 0.0001; muhat = 1.00 wmat = zeros(N+1,L); % 8001 filters wmat(1,:)=wn; for kk = 1: K % ensemble process xn =...

## Quadriphase barker sequences

inHello, I am looking for a quadriphase Barker sequence (a sequence whose elements are from the set {1,j,-1,-j} and which has a...

Hello, I am looking for a quadriphase Barker sequence (a sequence whose elements are from the set {1,j,-1,-j} and which has a periodic autocorrelation function whose maximum sidelobe magnitude

## should first coef of spiking decon Wiener filter be positive?

Spiking decon has been used in geophysics for over 50 years. An FIR Wiener filter is computed by Levinson recursion. The inputs are the...

Spiking decon has been used in geophysics for over 50 years. An FIR Wiener filter is computed by Levinson recursion. The inputs are the autocorrelation of the trace, and an impulse (1,0,0,0,...) as desired signal. It is based on certain assumptions, such as the wavelet being minimum phase and stationary (which are only approximations in reality). Now I have been looking at an open-source pac...

## Different Definitions for Inverse Fourier Transform

inIt's not completely standard, but I've usually seen a factor of 1/(2*\pi) in front of the integral for the inverse Fourier transform. I believe...

It's not completely standard, but I've usually seen a factor of 1/(2*\pi) in front of the integral for the inverse Fourier transform. I believe the theore says that this factor must be somewhere in the round-trip journey from forward transform to revers. It could be 1/sqrt(2*\pi) in front of both, or whatever. [papoulis] has the present in his definition of the autocorrelation function as ...

## Sine Wave autocorrelation, interpolation of phase

inHallo. For the purpose of measuring complex impedances i need to compare the phase of two copies of a sinewave over a number of periods. The...

Hallo. For the purpose of measuring complex impedances i need to compare the phase of two copies of a sinewave over a number of periods. The sinewave is generated in the same µC. Frequency is known and stable. The original and the shifted signals are sampled by a double synchr. ADC. The phase shift is the base for calculation of the complex Z of a load. I have implemented an (auto-)correlatio...

## each PMEPR has a distinct waveform?

hi all, while i am reading abt Peak Power reduction from Hanzo book pg 336. he described that a AA ( Aperiodic Autocorrelation) and its...

hi all, while i am reading abt Peak Power reduction from Hanzo book pg 336. he described that a AA ( Aperiodic Autocorrelation) and its transfroms ( actually circular shifted version of original waveform ) completely characterize PMEPR. so if one AA and its transforms have one PMEPR and one distinct waveform then can i conclude that the relation bet PMEPR and Distinct Waveform is one...

## IIR Wiener Filter in Matlab

inI am attempting to code an IIR wiener filter for system identification in Matlab, but I am currently having some difficulty with the theory......

I am attempting to code an IIR wiener filter for system identification in Matlab, but I am currently having some difficulty with the theory... Can someone please clarify? To find the spectral factorization, my understanding is that I take the roots of the autocorrelation sequence, then select those whose magnitude fall within the unit circle? Does anyone have any example IIR Wiener Matlab sc...