### Charles Rader (@CharlieRader)

Yes John_G, I had a copy of Abramovitz and Stegun, soft cover, $4 and with enough scotch tape I kept it usable for over fifty years, and after the front and back...

Forget about stereo. You have two real functions, f(n) and g(n).If you want to compute F(k) and G(k) there is a less costly way to compute two separate FFTs. Let...

I think what you mean to say is that the extra zeroes at z=0 do no affect the magnitude of the frequency response, contribute only a linear phase.

Safwan, I'm sorry if this is a rather picky point, but what you refer to as an all-pole filter has two zeroes at z=0. Multiply numerator and denominator of H(z)...

I would do exactly what you did. But if you do try any derivation analytically, you should use modular arithmetic algebra.

I don't understand what this has to do with DSP (Digital Signal Processing). You can't have continuous signals in DSP. They must be sampled and, usually, quantized.So...

Why have you limited yourself to a complex pole pair? Maybe try a Bessel filter. What bandwidth do you need? How much attenuation can you stand?Or try a non-recursive...

I have known about this for decades, but never saw it called an integer approximation. In the early days of my career, a square root operation was a big expense,...

In the screen shot provided you say the blue waveform is the input. It appears to pass through (0,0) so it looks like a sine function. (Unless the vertical axis...

You don't seem to have a vertical scale on the plot (or horizontal either, but that doesn't matter). I assume that the sine wave input goes from -1 to 1, e.g. x=sin(kn)...

There are all sorts of things that can be considered DSP. Certainly, if you want to process a measured signal without constraints of how fast, you don't need to...

Hi, I don't know if this will help you. Define a rectangular coordinate system with the radar at the origin. By definition, the center of the beam is a zero-thickness...

Do a search on the phrase "Gray code". It's a method of encoding positive binary numbers so that each two consecutive numbers differ in their encoding by a single...

It took me a while to understand that the hundred George took out of his pocket, ruefully, was Jody's tip.

Not my area of expertise, but I'll comment anyway. Optical frequencies are many orders of magnitude higher than radio frequencies. That means that a very very tiny...

Your angles 60.9 deg and 29.05 deg add up to 90 deg within a probably rounding error. The phase has not been "twisted" but reflected.

52 bits should be sufficient. I suggest that you look at Signal Processing Magazine, March 2009, at Rick Lyons' "DSP Tips and Tricks". The issue that concerns you...

You are exactly right. I said that in my first reply, in which I showed how to get away with a 2:1 speed reduction, then suggested that you could use the same...

Write the z-transform of the transfer function. H(z) = 1/(1-az^{-1})Multiply the transfer function by (1+rz^{-1})/(1+rz^{-1}) which is 1. Choose r=-a.Now the...

cthys, if I may change the subject:The usual way of presenting an impulse response is as plots of the real part and the imaginary part of a time sequence.Whenever...

This is a fairly complicated answer. Let me apologize that I don't know the programming language for your testing code.My first concern was that I don't know what...

I assume that the data originally came from an A/D converter with some number of bits. If no further processing was done after the recording, such as filtering,...

The only examples I see with sign reversals of phase are for n=1 and n=5, which are frequency bins n-1=0 and n-1=4. These are both, correctly, negative real numbers....

jms_nh, it took me years to understand what you just wrote about. What is white noise? My initial idea of a spectrum was rather simple. You start with a time function...

It would help to know more about what you want. Do you want to generate one indefinite length stream of random numbers? Or do you want to generate a finite length...

You have said several times that you are sure that the computation from A to B is correct. We are not sure, however, that we understand the sense in which you mean...

It should be a matter of a few seconds to do. Take the data in D, and create a new file which puts the last half at the front and the first half at the back, a 32...

kaz, this may help. The only difference between the DSP of a real sequence and the inverse DFT of the same real sequence is a scale factor and the sign of the...

OK, so you started with curves A and by algebra and calculus you computed curves B which are the time response (you call it a spatial response, makes no difference...

Joe, I may be beating my own drum here, but I do have some thoughts to share.First, if an input x(n) is fed into two causal time invariant linear systems, H_1(z)...

I think you have to express your requirement more carefully. What exactly is a precise delay filter? If the input and the output of the filter have the same sampling...

The ringing you refer to is because your approach creates a filter frequency response which has a discontinuity. I'm using the word discontinuity incorrectly because...

In any modulation system for which the constellation of possible signals, if there are several constellation members with the same angle but different amplitudes...

Westrace, perhaps I am guilty of requiring you to be too precise, but usually the matched filter is used to identify a signal buried in noise. Unless the noise is...

I need some clarification. At the receiver you have some signal x[n] that you want and another signal y[n] which is a pure sinusoid. y[n] is unwanted. You only...

The 90 degree FIR half-band filter, zeroes rotated by ninety degrees, gives you an FIR Hilbert transformer approximation, phase a perfect 90 degrees, but it is not...

gretzteam, I haven't seen it before, but it gives a specific case, which I would call N=9. It's a 90 degree case. There's a set of formulas for the 90 degree case...

I did try that. It let me choose a file, which I did. But apparently there is some other step because the file I chose didn't seem to show up. Using drop and...

Thanks emeb. Is it common knowledge how to design such filters? I am using a mapping based on Jacobian elliptic functions and the resulting designs are provably...

Almost sixty years ago I needed an all-pass recursive digital filter with two outputs, such that the phase difference between the outputs was a very good approximation...

Zack, I'm not familiar with the application and didn't even know what the initials LTE stood for. (Side comment - the first time you use a a letter sequence abbreviation,...

I began working after getting my Masters degree in 1961, with the idea that I would work for a few years and then get a PhD. I knew I wanted to do research. But...

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