Frequency Domain Analysis - The Z transform Flashcards
What are the main reason for using Z Transforms
- compact and convient way of describing DSP systems 2. widely used by DSP engineers 3. pole-zero great for vizualising stablility and characteristics
What is the definition of the Z transform
Describe what “recovering” a signal means when dealing with Z transforms and the two ways it may be done…
going from X(z) to the signal x[n]. Using partial fractions to put it in the form it can be used (via the table), producing the inverse z transform function an then superimposing 3 components before performing long division on the to get the required power series..
The second method is called - using a recursive algorithm….
Describe how partical fractions are performed
Describe how to do long division
What is the symbol for the transfer function
H(z)
What is the transfer function equivalent of?
The transfer function H(z) is equivalent of the frequency response function H(Omega)
What is the definition of the inverse function?
What is the inverse transfer function used to work out?
The inverse transform of X(z)H(z) giving an output of y[n]
What are the two more easy to use altneratives to the formal inverse defintion to calculate the inverse transfom of X(z)H(z)
- Express X(z) as a power series
- Use the look up table of z-transform pairs
Unilateral Z transforms table pairs
waveform | signal x[n] | Spectrum X[z] | Z planes and zeros | - 8 rows
Unilateral Z transform properties
property or operation | Signal | Z Transform | - 8 rows
What can a H(z) function be equivalent to?
An eqivilent time domain function (a difference equation)
Describe the final value theorem and the equations that support it (Picture of Pge 106 in book)
Describe what an argand diagram is..
It a circular diagram that both poles and circles can be put n in order to visualise the stablity and frequency response characteristics
What does substituting exp(jΩ) do for z give?
The frequency response of the system i.e H(z) becomes H(Ω)
Describe what operations are being performed to get the weird spiking graph
This graph represents fourier transform in the z-plane giving |H(Ω)| (the magnitude of the spectra signal)
What is the magnitude of the spectra signal eqaul to {|H(Ω)|}
The product of all the zero-vector lengths divided by the product of all of the pole vector lengths
Visualose the freqeuncy response of an LTI processor - That is |H(Ω)| which is equal to the sum of the zero-vector lengths divided by the pole vector lengths - where gain may be afactor but will not alter te shape.
Describe why first and second order z- transforms are useful
It is done to summarise the performance of a pole-zero, frequency response and impulse response
Defintion of first order and second order z transform
Characteristic of a first order z transform
Characteristic of a second order system
Important First and second order equations
