## Forums Search for: Invariance

## DSP-impulse invariance method

inNow, I use the impulse invariance to design a lowpass filter. I need to find the H(s) from pole pairs. I don't know how toconvert H(s) to H(z)....

Now, I use the impulse invariance to design a lowpass filter. I need to find the H(s) from pole pairs. I don't know how toconvert H(s) to H(z). Can anyone help me? Thanks!! Laura

## Impulse invariance method

inI have a laplace transfer-function G(s)=k(1+sT)/s*2 which I need the discrete-time version G(z) using impulse invariance method. Using...

I have a laplace transfer-function G(s)=k(1+sT)/s*2 which I need the discrete-time version G(z) using impulse invariance method. Using partial fractions I get G(s) = c1/s + c2/s^2 c1=kT and c2=k However when I use Matlab c2d and select "impulse" it gives me a different version though the first term c1 is right. Matlabs second term c2 is negative. I assume for multiple pole...

## help regarding impulse invariance method !

inHi, i hav just studied the impulse invariance method & bilinear transform. In Impulse Invariance there is "many to one mapping" and hence...

Hi, i hav just studied the impulse invariance method & bilinear transform. In Impulse Invariance there is "many to one mapping" and hence aliasing takes place. while in Bilinear Transform there is "one to one mapping" and hence no aliasing. Actually what is the "one to one mapping" & "many to one mapping"? how it is related to aliasing?

## Question about IIR filter design using Impulse Invariance method

inI am designing low pass IIR filter using Impulse Invariance method. I've got transfer function H(z) which depends on impulse sample period...

I am designing low pass IIR filter using Impulse Invariance method. I've got transfer function H(z) which depends on impulse sample period T. I was asked to choose an appropriate impulse sample period T for H(z) such that the input signal x(t) = 5 cos(2pi(8000)t ? pi/3) ? 4 cos(2pi(40000)t + pi/2) sampled at a rate of Fs = 100 kHz has only the 8000 Hz sinusoid in the passband. I do...

## rotational invariance

inI am having difficulties to solve the following question. Would you please help me? suppose that X and Y are independent and each rotationally...

I am having difficulties to solve the following question. Would you please help me? suppose that X and Y are independent and each rotationally invariant on R^k a) Let X = X1 with Xi on R^k1 where i =1,2 and prove X2 - Each Xi is rotationally invariant in its own right - If Vi is in R[from K1 to K] with V'V = I, then V'X = X1 b) Let p denote any orthogonal projection with dim...

## Is complex-conjugation an LTI operation?

inGood morning all, This conundrum may be due to it being too early in the day for me to think clearly, so please tell me where I've gone...

Good morning all, This conundrum may be due to it being too early in the day for me to think clearly, so please tell me where I've gone wrong! It would appear to me that complex conjugation would satisfy the properties of linearity and time-invariance, and therefore could be categorised as an LTI operation. However, clearly it creates frequency content that was not present in the origin...

## Re: Blinded by math. Was "How does an inverter affect phase?"

inAndor wrote: > Jerry Avins wrote: > > ... > > > > > Such a definition can be via specification of the response for one > > > > > single...

Andor wrote: > Jerry Avins wrote: > > ... > > > > > Such a definition can be via specification of the response for one > > > > > single sinusoid, and requiring linearity and time-invariance. As soon > > > > > as you do that, the response at DC and Nyquist follows, and we can stop > > > > > quibbering and just look at the facts. > > You find a reasonable mathematical way to express an intuitively simple >

## Correcting Impulse Invariance Method

I'm trying to find out if the correction (Jackson, Nelatury, MecklenbrĂ¤uker) could improve the (IIM based) filter's magnitude response near...

I'm trying to find out if the correction (Jackson, Nelatury, MecklenbrĂ¤uker) could improve the (IIM based) filter's magnitude response near Nyqvist. Here's my c++ routine (which is used for to calculate various RIAA and non-RIAA filters by just changing the timeconstant values and samplerate): double a0, a1, a2, b0, b1, b2; double fs = 44100; //timeconstants (case RIAA): // frequency ->

## gain response

I have to design Chebyshev type I analog lowpass filter and transform it to digital filter using impinvar() and bilinear(). Then I have to plot...

I have to design Chebyshev type I analog lowpass filter and transform it to digital filter using impinvar() and bilinear(). Then I have to plot the gain response for both methods and do comparisons. However, the gain response take in the input of g of 20log10(H)?? function X = invariance(fs) fs = 100000; wp = 10000*2/fs; ws = 30000*2/fs; rp = 0.4; rs = 50; [n,wn] = cheb1ord(wp,ws,r...

## gain response

I have to design Chebyshev type I analog lowpass filter and transform it to digital filter using impinvar() and bilinear(). Then I have to plot...

I have to design Chebyshev type I analog lowpass filter and transform it to digital filter using impinvar() and bilinear(). Then I have to plot the gain response for both methods and do comparisons. However, the gain response take in the input of g of 20log10(H)?? function X = invariance(fs) fs = 100000; wp = 10000*2/fs; ws = 30000*2/fs; rp = 0.4; rs = 50; [n,wn] = cheb1ord(wp,ws,r...

## inverse laplace transform

inHi all I'm working on trying to model a non-linear system (described by a second order differential eqn) into a discrete IIR filter. I guess...

Hi all I'm working on trying to model a non-linear system (described by a second order differential eqn) into a discrete IIR filter. I guess I'm trying to follow the impulse invariance IIR filter design method. In the laplace domain, the transfer function looks like this H(s) = a^2/(s+a)^2 I tried looking up laplace transform tables to find the time domain form for this and the closes...

## How to improve filter quality at low fs

inHello, and thanks for fixing the posting problem! I'm using this (Impulse Invariance Method based) code for to calculate coefficients for...

Hello, and thanks for fixing the posting problem! I'm using this (Impulse Invariance Method based) code for to calculate coefficients for biquad digital filter (for RIAA and non-RIAA de-emph.). double a0, a1, a2, b0, b1, b2; double fs = 44100; //timeconstants (case RIAA): // frequency -> time conversion 1/(2*pi*fc) (= R*C) //poles double p1 = 3180e-6; // 1/(2*pi*50.05Hz) double p2 = 75

## Periodicity , shift invariance and stationarity

inContinuing with Tim Wescott's article I would like to ask following question Periodic signals are defined as signal which repeats after...

Continuing with Tim Wescott's article I would like to ask following question Periodic signals are defined as signal which repeats after certain period i.e mathematically, f(t)=f(t+p), where p is time period (say, time domain signal). Can this signal be called as "shift invariant"? Also some papers write "shift invariant" as "stationary" - meaning statistical property such as mea...

## Linear System Properties?

inHi, I have some simple questions about the properties of linear systems. In a linear System we have to assume the properties of homogeneity,...

Hi, I have some simple questions about the properties of linear systems. In a linear System we have to assume the properties of homogeneity, additivity and shift invariance. In a DSP book I read that from these properties you can conclude that a sine wave as input will always produce a sine wave on the systems output with the same frequency. I can't really see what speciality of sine waves ...

## What is the standard output of a low pass digital filter design program?

inHello, I wrote a small program for class to design a low pass digital filter. it is an IIR filter designed using Butterworth. We are given...

Hello, I wrote a small program for class to design a low pass digital filter. it is an IIR filter designed using Butterworth. We are given the specifications, and I have generated H(s) and H(z) (using impulse invariance, and using bilinear methods). What is considered as a "standard" output to print as a result of such a design run? I am now printing the pole locations for Butterwor...

## impulse response of a nonlinear filter

inHello forum, if a time-invariant (zero memory) nonlinear filter is fed with a delta impulse, it will output a certain output. That output...

Hello forum, if a time-invariant (zero memory) nonlinear filter is fed with a delta impulse, it will output a certain output. That output will be the same no matter when the impulse is applied due to time invariance.... Superposition (convolution) is not valid for nonlinear system. Is there however some generalized impulse response concept for nonlinear systems? After all, nonlinear...

## realising an analog transfer function in digital domain with minimum error

inHi, I am trying to design an analog transfer function in digital domain. I tried using various methods like impulse invariance and...

Hi, I am trying to design an analog transfer function in digital domain. I tried using various methods like impulse invariance and bilinear transform. But when I used bilinear transform I am getting error of around 1db at nyquist frequency. Are there any other better methods??? Thanks --------------------------------------- Posted through http://www.DSPRelated.com