### Detlef Amberg (@Detlef _A)

Detlef Amberg has a Ph.D. in EE. He is living in Berlin and working on the design of telecommunications equipment. His professional interests include math, signal processing, embedded systems, digital/analog electronics and software defined radio.

## Fitting a Damped Sine Wave

A damped sine wave is described by

$$x_{(k)} = A \cdot e^{\alpha \cdot k} \cdot cos(\omega \cdot k + p)\tag{1}$$

with frequency $\omega$ , phase p , initial amplitude A and damping constant $\alpha$ . The $x_{(k)}$ are the samples of the function at equally spaced points in time.

With $x_{(k)}$ given, one often has to find the unknown parameters of the function. This can be achieved for instance with nonlinear approximation or with DFT – methods.

I present a method to find the...

## Re: mitigating phase shift

THX, yes, the whole plan, ( narrow bandpass, than PLL)  is a misconcept. The noise mitigation has to be a part of the PLL. And yes, I want to multiply (mix) incoming...

## mitigating phase shift

Hi, I want to PLL on the line voltage, here in Europe 50Hz. I have a noisy signal and i use a prefilter with a complex pole pair at 0.999*exp(+/- j*2*pi*50/10000)....

## Re: How "Oversampling" works for determining max amplitude for audio applications?

Very interesting question. You sample a bandwidth limited signal with respect to Nyquist and you have two samples, x(k) and x(k+1). What is a lower boundary for...

## Re: Help with polynomial zeros

Hi,your 'for' loop gets much shorter with these two linesff1 = (exp(j*2*pi*[frb -frb]/Fs));fff = poly(ff1);But that does not bring you out of the numeric troubles...

## Re: Recover signal from the real part of IFFT

Hi,IFFT of a spectrum with the 'upper' half of the frequencies zeroed out results in a complex time signal, called 'analytic' signal with 90° phase offset between...

## Re: OFDM Pilot Detection

Hi, identify a FFT bin with constant amplitude and phase. This is a pilot tone.CheersDetlef

## Re: FSK demodulation with Doppler correction

Hi,the standard approach to FSK demodulation: square the samples, so you get a carrier at the symbol frequency. You track this carrier with a PLL and downmix the...

## Re: Why low number of subcarriers is needed for high path loss scenarios​ ?

In a DSL szenario with many carriers and high PAPR you just let the amplifier clip, which results in error bursts. These errors are spread over time with the descrambler...

## Re: PAPR (peak to average power ratio)

As said, OFDM and other modulation schemes show an inherently high PAR, ie. you have that naughty peak at times. This will be clipped by your cheap power amplifier,...

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