### Harry Commin (@weetabixharry)

I am a British electronic engineer with a background in implementing DSP in FPGAs and ASICs. I finished my PhD in Electronic Engineering at Imperial College London in 2013 and am currently working for a small FPGA design service company in Zurich, Switzerland.

## Generating Partially Correlated Random Variables

March 23, 201921 comments
IntroductionIt is often useful to be able to generate two or more signals with specific cross-correlations. Or, more generally, we would like to specify an $\left(N \times N\right)$ covariance matrix, $\mathbf{R}_{xx}$, and generate $N$ signals which will produce this covariance matrix.

There are many applications in which this technique is useful. I discovered a version of this method while analysing radar systems, but the same approach can be used in a very wide range of...

## Re: How do I produce a covariance matrix from IQ samples?

If you're familiar with MATLAB, then you can work through the full example of MUSIC I originally posted here back in 2013.The code is heavily commented and doesn't...

## Re: Is a frame-based processing possible for biquad filters?

There doesn't seem to be anything fundamentally different about "frame-based" processing in MATLAB. The frames are not independent. Simply, the sample data is collected...

## Re: Can an FFT be shared for spectral estimation and linear filtering?

@kaz My sample rate is 4 GSps. So I was saying I can't clock my FFT core at 8 GHz (or 16 GHz, with 1/2-overlap) and reuse it for the IFFT. I will clock it at 250...

## Re: Can an FFT be shared for spectral estimation and linear filtering?

@kaz My FIR filters are large, so DSP slice utilization is reduced immensely by implementing them in the frequency domain. (By a rough calculation, the reduction...

## Re: Can an FFT be shared for spectral estimation and linear filtering?

@samecues I have read that WOLA article and some other papers related to WOLA. However, I cannot see anything related to a simple linear filter (like a lowpass filter).You...

## Re: Can an FFT be shared for spectral estimation and linear filtering?

@samecues You understood exactly. And my filter is just a lowpass filter.If I understood you correctly, you are saying that by changing my Hann "analysis" window...

## Re: Can an FFT be shared for spectral estimation and linear filtering?

@kschutz I'm not specifically tied to Welch's method and I had also considered your "poor man's power spectrum". It's something I would probably resort to if I...

## Can an FFT be shared for spectral estimation and linear filtering?

I am familiar with the overlap-add and overlap-save methods for computing linear convolutions.I am also familiar with Welch's method for estimating power spectral...

## Re: 2D-MUSIC algorithm for range-azimuth mapping in MATLAB

You haven't said what the problem is. Since you are just using MATLAB's pre-packaged functions, I suggest you read the MATLAB documentation (which is typically quite...

## Re: Coherent Sources for DOA estimation

I can, but your questions are too general. The literature on this topic is vast, so you will need to narrow down what it is you are trying to understand.Do you mean...

## Re: Off by one windowing

I'm not sure if you're aware that we commonly use at least 2 different symmetries in window functions. You mentioned (or implied) that you don't have a practical...

## Re: time recovery algorithm and CORDIC

@Mannai_Murali Why not share your code here in the forum so someone else may benefit from it in the future?@Ali23 Do you specifically need an example in MATLAB or...

## Re: time recovery algorithm and CORDIC

The rough idea is that the +/- sign of the error should tell you to either increase or decrease the sample rate in your receiver.The point is that the sample clock...

## Re: How can I calculate the doa for acoustic signals by applying the Music algorithm in MATLAB?

I can't really say much about the first figure. I guess it shows your signal is not all zeros, which is a good start.Your second figure shows effectively all zeros...

## Re: How can I calculate the doa for acoustic signals by applying the Music algorithm in MATLAB?

Please attach your graphs and code for conventional beamforming.It is only a small modification to convert that to use MUSIC.

## Re: How can I calculate the doa for acoustic signals by applying the Music algorithm in MATLAB?

I don't know what your hardware setup is, but it is surprising to me that you talk about sound recordings and the speed of light. I would expect the speed of sound...

## Re: How can I calculate the doa for acoustic signals by applying the Music algorithm in MATLAB?

If the other methods are working, then I'm not sure exactly what you want to know. Presumably, you have already been able to calculate the received signal covariance...

## Re: How can I calculate the doa for acoustic signals by applying the Music algorithm in MATLAB?

I'm not sure if I understand your question. If you already have some received data, then you don't need to generate it, so you can ignore sections (1) and (2) of...

## Re: How can I calculate the doa for acoustic signals by applying the Music algorithm in MATLAB?

Your calculation of the direction matrix A looks incorrect to me. This matrix should include information about the source directions and the geometry of your sensor...

## Re: What is the maximum output amplitude of an IIR filter?

@kaz Quantization doesn't change anything.We can constrain the maximum input amplitude to be any number (quantized or not - it doesn't make any difference).And rounding...

## Re: What is the maximum output amplitude of an IIR filter?

@kaz If you don't impose any constraints on the input signal, then the output signal can be infinitely large (e.g. if you multiply all of your input signals by Inf).Therefore,...

## Re: What is the maximum output amplitude of an IIR filter?

@kaz For a FIR filter, the impulse response (y) is the filter (h). At the end of your code, if you compare y and h, you will find they are identical. So you have...

## Re: What is the maximum output amplitude of an IIR filter?

@hirnprinz Thank you very much for sharing that article. That was exactly the track I ended up going down. After reading the article, it seems so obvious, but I...

## Re: What is the maximum output amplitude of an IIR filter?

@kaz As the name suggests, an exact representation would typically need infinitely many FIR taps (in the same way that we would need an infinite sample rate and...

## Re: What is the maximum output amplitude of an IIR filter?

@dszabo This worked really well (once I remembered to flip the order of the FIR taps to get the convolution in the correct order).I wasn't really sure how to choose...

## Re: What is the maximum output amplitude of an IIR filter?

@dszabo Ah, now I see what you're saying! Great idea. I'll give it a try.

## Re: What is the maximum output amplitude of an IIR filter?

Yes, this is basically what I am researching.If we reduce the input amplitude, then the question remains: "by how much should it be reduced (for a given filter)?".If...

## Re: What is the maximum output amplitude of an IIR filter?

@philipoakley Thank you. This sounds logical. I need to mull it over, but I think this is going in the right direction...

## Re: What is the maximum output amplitude of an IIR filter?

@kaz I have written fixed-point software models that include the internal rounding.I have tested with a wide variety of input signals (including Gaussian noise,...

## Re: What is the maximum output amplitude of an IIR filter?

@Slartibartfast With a FIR filter, I feel like I have a clear idea about how to make this design decision. I can calculate exactly what the maximum output value...

## Re: What is the maximum output amplitude of an IIR filter?

@dgshaw6 In my current work, I am only dealing with 1st order filters. Does your rule of thumb apply there too?With all of the test signals I have tried, I haven't...

## Re: What is the maximum output amplitude of an IIR filter?

@dszabo An impulse will not typically produce the largest possible amplitude at the output of the filter (in the time domain).

## Re: What is the maximum output amplitude of an IIR filter?

@kaz As I said in my original post, even if gain (in the frequency domain) is < 0dB across all frequencies, the output amplitude (in the time domain) can still...

## Re: What is the maximum output amplitude of an IIR filter?

@philipoakley Maybe I can understand better using a specific example. I have a filter with this transfer function:$$H(z) = \frac{1 - z^{-1}}{1 - Az^{-1}}$$where...

## What is the maximum output amplitude of an IIR filter?

When implementing a fixed-point digital filter, I need to think about overflow/saturation. For a FIR filter, the maximum +/- output values (OUTPUT+ and OUTPUT-) are...

## Re: hardware FFT coefficients .vs. np.numpy.fft.rfft

I didn't fully understand your description, but please note that the ideal way to fix this is in the time domain (by aligning the samples fed to your software FFT...

## Re: hardware FFT coefficients .vs. np.numpy.fft.rfft

Are the time-domain samples aligned identically into both the hardware and software FFTs?A shift in the time-domain corresponds to a phase ramp in the frequency...

## Re: Understanding MUSIC algorithm and applying it in 2 cases

If there is only one signal arriving from one direction, then M=1.If there is one signal source, but arriving from multiple directions (due to reflections/echoes),...

## Re: Understanding MUSIC algorithm and applying it in 2 cases

If a simple Matlab implementation would be instructive, then take a look at this forum post I wrote some years ago.Later in the same thread, I expanded it to 2D...

## Re: Matlab/Octave loop vectorization

@kaz I assume it's because Matlab is an interpreted language, so there isn't a compiler doing that kind of optimization.

## Re: Autocorrelation of OFDM Signal

The sequences don't repeat indefinitely in WiFi, or there would be no way to transfer any information. WiFi is a bursty signal, so some useful "preamble" is prepended...

## Re: Autocorrelation of OFDM Signal

If I understand correctly, you expect the "true" autocorrelation peak to correspond to the offset for which all the cyclic prefixes in the capture are aligned with...

## Re: Autocorrelation of OFDM Signal

Are you sure these built-in autocorrelation functions do what you want? I suspect they don't, unless you are being pretty careful about how you feed them data.Or...

## Re: Autocorrelation of OFDM Signal

Is it possible that the sequence you are autocorrelating contains a repeating, repeating pattern? (i.e. something that repeats several times).This is pretty common,...

## Re: Digital down-conversion and cross-talk

The thing I feel more worried about is whether a real-valued mixer is definitely suitable for your application.However, as per emeb's reply, I don't feel worried...

## Re: Design a preamble structure for OFDM

Everything in those Matlab scripts is specified explicitly in the 802.11 specification. The comments in the Matlab code refer to the part of Annex I (e.g. "I.1.3.2"...

## Re: Design a preamble structure for OFDM

Have you seen Annex I of the 802.11 PHY standard? This takes you through every step of the 802.11a/g modulation process to make sure you get everything exactly right....

## Re: Curve Modelling

If I understand what you are trying to do, then I don't think the method of finite difference is the best choice. As far as I know, the method of finite difference...

## Re: Curve Modelling

If you use Matlab, then I think these 2 very simple lines of code sum up Least Squares polynomial curve fitting very well:C = bsxfun(@power, (0:L).', (0:N)); a =...

## Re: How to parallelize polyphase FIR resampling filters

@kaz I understand the principle of rational-ratio resampling, but the challenge here lies in determining (in closed form) where the redundancy will be. Or, equivalently,...

## Re: How to parallelize polyphase FIR resampling filters

@kaz I don't think I follow your explanation. Could you give a simple example? For example, if I want 6 parallel inputs and 8 parallel outputs (interpolation by...

## Re: How to parallelize polyphase FIR resampling filters

@Slartibartfast Fixed resample rate. The resample rate can even be 1. For example, the most popular structure in the literature seems to be the "two-parallel FIR...

## How to parallelize polyphase FIR resampling filters

I am struggling to find a good reference for implementing parallel rational-ratio FIR resampling filters. By "parallel", I mean a high-throughput hardware filter...

## Re: What is the cost of a typical MSEE degree?

My 4-year "undergraduate Masters" at Imperial College London (2005 - 2009) cost around £3,600 total in tuition. I believe it's now £9,000/year tuition for EU...

## Re: Signal Generation methods and alternatives

Does N change only at compile time, or at run time too?Do the frequencies that you want to generate change only at compile time?Could you explain a little more about...

## Re: Low cost audio DSP Exploration

Thanks for the clarification. I think an extra sentence in the original post to provide any kind of context would have eliminated any doubt. It's now obvious it...

## Re: AD9601 with 200MSPS connected to DSP

I agree that this is likely to be a problem in many applications. However, not necessarily, since it depends what Yash5 wants to do with the data. I don't think...

## Re: AD9601 with 200MSPS connected to DSP

I think the most direct answer to your question is that you could buy the smallest, cheapest FPGA on the market and use it to simply deinterleave (split) your samples...

## Re: Somewhat Off Topic: Manipulating a PDF File.

I second the "print to pdf" option suggested by rrlagic. A possible downside to this is that you will lose any metadata (such as links within the document).My favourite...

## Re: half and quarter sample meaning

Sounds like interpolating.  What is the context?I second that. In fact, that's more or less word-for-word what I was going to reply.

## Re: Fixed point filter gain

This is not correct in general, and I don't think @dsplearn has provided enough information to be sure that it is definitely suitable for them.If, for example, your...

## Re: Fixed point filter gain

I would like to add that "discarding" is not your only option when you want to divide a fixed-point number by $2^n$. Discarding in this context is referred to as...

## Re: What is the frequency response of a resampling filter?

@neiroberI could be misunderstanding, but there may also be different (equally valid) ways to look at it. In the summary, I see Steps 1 and 2 as moving all the FIR...

## Re: What is the frequency response of a resampling filter?

@neiroberI read through your post quickly and, if I understand correctly, you are saying that the multi-stage decimator is still equivalent if we reorder the filtering...

## Re: What is the frequency response of a resampling filter?

@neiroberGreat, thanks Neil. I am amazed (and a little embarrassed) that I didn't find your post in any of my Google searches.This looks like really valuable material...

## Re: What is the frequency response of a resampling filter?

@Rick LyonsBrilliant. Thank you for the excellent response. Your article looks like exactly what I was looking for from the start (if only I had entered better search...

## Re: What is the frequency response of a resampling filter?

Ahhh, I see. That makes sense. I'm just now starting to realise what that lecture 13 years ago was about!If a system is not LTI, I'm a bit lost... In the case of...

## Re: Auto Correlation in DSP processor

Firstly, I would like to offer my deepest condolences that you have to work with LabVIEW. In my opinion, it is quite nice for connecting simple pieces of hardware...

## What is the frequency response of a resampling filter?

I am trying to characterise the combined frequency response of several (FIR) decimating filters connected together in series. I basically want to be able to tweak...

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