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

Detlef Amberg July 3, 20155 comments

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: Help with polynomial zeros

Reply posted 2 months ago (08/07/2021)
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

Reply posted 6 months ago (04/23/2021)
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

Reply posted 12 months ago (10/30/2020)
Hi, identify a FFT bin with constant amplitude and phase. This is a pilot tone.CheersDetlef

Re: FSK demodulation with Doppler correction

Reply posted 1 year ago (09/24/2020)
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...
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)

Reply posted 5 years ago (04/13/2017)
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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