Retired, worked at MIT Lincoln Laboratory 1961-2020. Involved in digital signal processing, speech, satellite reliability and quantum computing.

## Re: Modulation in laser satellite communication

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...

## Re: Complex IF

$atan(x)=\pi/2 - atan(1/x)$

## Re: Complex IF

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.

## Re: Can you find the illegal step?

Going from step 3 to step 4, you divided by (a-b). Division by 0 is not meaningful.

## Re: Is there any reliable implementation method of IIR filters with pole positions very close to the unit circle?

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...

## Re: Digital IIR Parallel Implementation

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...

## Re: Digital IIR Parallel Implementation

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...

## Re: Impulse response in OFDM system using IFFT

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...

## Re: How to test my FFT implementation?

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...

## Re: Calculating the Effective bit resolution from a .WAV recording?

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,...

## Re: Non-zero DFT components where zero is expected?

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....

## Re: How to synthesize band-limited noise?

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...

## Re: How to synthesize band-limited noise?

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...

## Re: Inverse DFT of frequency domain signal sampled from a continuous function

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...

## Re: Inverse DFT of frequency domain signal sampled from a continuous function

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...

## Re: Inverse DFT of frequency domain signal sampled from a continuous function

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...

## Re: Inverse DFT of frequency domain signal sampled from a continuous function

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...

## Re: Single vs split Hilberts

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)...

## Re: fractional delay filter for non real time applications

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...

## Re: fractional delay filter for non real time applications

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...

## Re: Question regarding match filter implementation in receiver

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

## Re: Question regarding match filter implementation in receiver

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...

## Re: Auto-Correlation based Carrier Frequency Recovery

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...

## Re: Digital Filters that have prescribed phase shift

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...

## Re: Digital Filters that have prescribed phase shift

Thanks, that seems to work.

## Re: Digital Filters that have prescribed phase shift

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...

## Re: Digital Filters that have prescribed phase shift

It's a pdf file. It's a plot made by GNU octave, which is a MATLAB equivalent system that's free.

## Re: Digital Filters that have prescribed phase shift

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...

## Re: Digital Filters that have prescribed phase shift

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...

## Digital Filters that have prescribed phase shift

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...

## Re: LTE IFFT Sampling and Nyquist Rate

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,...

## Re: PhD in E.E. is it really worth it

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...

## Re: Who discovered the math of the digital polar discriminator?

I don't know if it is as simple as this. If a waveform has the componentx(nT) = Aexp(j n omega T) then the product of the sample with its predecessor's complex conjugate...

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