Introduction to Digital Filters

A discrete time signal is the ___ of scaled and _ --- impulses

sum of scaled and delayed impulses

Discrete time systems

A systems that maps input sequence to an output sequence

superposition

weighted sum of inputs = weighted sum of outputs

A linear systems obeys the principle of

superposition i.e weighted sum of inputs = weighted sum of outputs

The principle of superposition consists of

Additivity and Homogeneity (scaling)

Time invariant systems

a time shift in the input results a in a corresponding time shift in the output

Discrete time signal representation is given as

x[k]δ[n-k]

LTI Systems response is aka the

Convolution sum

impusle response

systems output given to an impulse input

in the time domain, LTI systems are characterised by their

Impulse Response

Convolution properties

Commutative

Associative

Distributive

\

Constant Coefficient Difference Equations

y[n] = ∑bx[n-k] - ∑ay[n-k]

weighted sum of current input and previous input and output

The order of the filter and the length of the filter is given as

N and N+1

IIR

Infinite Impulse Response

FIR

Finite Impulse Response

IIR filter is one which has dependence on previous output

Yes it has, The FIR doesn’t depend on previous outputs

IIR filter has a finite response to a single impulse

No it has unlimited response but FIR has finite response

Casual system depends

only on the current and present inputs but not future inputs

Response of the LTI system to an sinusoidal input is

the scaled magnitude and phase version of the sinusoid

y[n] = H(Ω)exp(jΩn)

exp(jΩn) is the ___ AND H(Ω) is the _--

Eigenfunction and Eigen value

to ensure stablity in the z domain

the poles must be within the unit circle

\

if p1 > 1 in a first order c transform what occurs

exponential growth in Output.

y[n] = p^n for n >= 0