# ELV

Einführung in die digitale Signalverarbeitung Teil 1/8

# Rest

Delta-Distribution (Dirac-Funktion, Stoßfunktion, Impulsfunktion , Einheitsimpulsfunktion)

Basisband
Grenzfrequenz
Unterabtastung
Frequenzspektrum
Gleichwert, Gleichanteil, DC-Wert, DC-Komponente

Zeitdiskretes Signal
Abtastrate fs in [Samples / s], oder Abtastfrequenz [Hz]

### Regelung

• Steuerung
• Strecke
• Anregungsfunktion => Sprung, Rampe, Rechteckimpuls, Dirac-Impuls
• Systemantwort

#### Christian Münker

DSP auf FPGAs: Kap. 1-1 Grundelemente von zeitdiskreten Systemen

#### Jörg J. Buchholz

1.3 Spezielle Anregungsfunktionen und Systemantworten

### MATLAB

#### Common

conv, Convolution and polynomial multiplication

#### Symbolic Math Toolbox

numden, Extract numerator and denominator
ztrans, Z-transform
pretty, Prettyprint symbolic expressions

#### Control System Toolbox

sisotool, Control System Designer

tf, Create transfer function model, convert to transfer function model
zpk, Create zero-pole-gain model; convert to zero-pole-gain model
filt, Specify discrete transfer functions in DSP format
impulse, Impulse response plot of dynamic system; impulse response data
ss, Create state-space model, convert to state-space model
evalfr, Evaluate frequency response at given frequency
tfdata, Access transfer function data

#### Signal Processing Toolbox

fvtool, Open Filter Visualization Tool
digitalFilter class, Digital filter

zplane, Zero-pole plot
freqz,Frequency response of digital filter (Signal)
ss, Convert digital filter to state-space representation
fir1, Window-based FIR filter design
zp2tf, Convert zero-pole-gain filter parameters to transfer function form
tf2zp, Convert transfer function filter parameters to zero-pole-gain form
tf2sos, Convert digital filter transfer function data to second-order sections form
tf2zpk, Convert transfer function filter parameters to zero-pole-gain form

#### DSP System Toolbox

freqz, Frequency response of filter (DSP)

Subplot_1

% Calculate the data for the plots
fm = 20e3;
fc = 100e3;
tstep = 100e-9;
tmax  = 200e-6;
t = 0:tstep:tmax;
xam = (1 + cos(2*pi*fm*t)).*cos(2*pi*fc*t);

T = 1e-6;
N = 200;
nT = 0:T:N*T;
xn = (1 + cos(2*pi*fm*nT)).*cos(2*pi*fc*nT);