# LZI-System

Instruction Manual (German)

LZI - System

LTI means Linear Time Invariant. The transmission behavior of an LTI-System can be fully described by its transfer function or impulse response.

$Y(f)=X(f)⋅H(f) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywaiaacI cacaWGMbGaaiykaiabg2da9iaadIfacaGGOaGaamOzaiaacMcacqGH flY1caWGibGaaiikaiaadAgacaGGPaaaaa@429B@$
$y(t)=x(t)∗h(t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacI cacaWG0bGaaiykaiabg2da9iaadIhacaGGOaGaamiDaiaacMcacqGH xiIkcaGGObGaaiikaiaacshacaGGPaaaaa@41C8@$

The following transfer function is given:

$H(f)= 1 1+j(f/ f H MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamisaiaacI cacaWGMbGaaiykaiabg2da9maalaaabaGaaGymaaqaaiaaigdacqGH RaWkcaWGQbGaaiikaiaadAgacaGGVaGaamOzamaaBaaaleaacaWGib aabeaaaaaaaa@4193@$.

This is equivalent to a RC-low pass with the 3 dB cutoff frequency

This LTI-System is analyzed by a harmonic oscillating signal with constant amplitude and variable frequency. The resulting signal is a damped and phase-shifted harmonic oscillation.

$y(t)= x ∧ |H(f)|cos(2π f 0 t−b(f)) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garmWu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYd f9irVeeu0dXdh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqaq =JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vqpWqaaeaa biGaciaacaqabeaadaqaaqaaaOqaaiaadMhacaGGOaGaamiDaiaacM cacqGH9aqpdaWfGaqaaiaadIhaaSqabeaacqGHNis2aaGccaGG8bGa amisaiaacIcacaWGMbGaaiykaiaacYhaciGGJbGaai4Baiaacohaca GGOaGaaGOmaiabec8aWjaadAgadaWgaaWcbaGaaGimaaqabaGccaWG 0bGaeyOeI0IaamOyaiaacIcacaWGMbGaaiykaiaacMcaaaa@4C4D@$

You can also choose from a variety of input signals and observe how the LTI-system affects the signal.