Frequency response, Frequency Response

Frequency response

Assignment Help Electrical Engineering

Reference no: EM13667012

Frequency Response
Consider numerical differentiation seen in Assignment #1 and used in an article appearing in The American Journal of Cardiology, 1991; 67: 965-975.
“Each sampled signal was differentiated according to the formula
y[n] = .5{x[n + 1] − x[n − 1]} + (1/8){x[n + 2] − x[n − 2]}
This differentiation has the convenient characteristic of shifting the frequency content of the signal upward in a precise mathematical way.”Using linear systems concepts, you can quantify the “precise mathematical way.”
(a) Find the the frequency response, H(e^jω).
(b) Is this discrete time system a good approximation for differentiating a continuous-time signal?For some inputs? For all inputs? For no inputs? Explain your claim.
Hint: In the frequency domain, consider both the magnitude and phase response; recall that d dtx(t) has Fourier transform jωX(jω). Let sampling period be T seconds.
(c) How would you make this system causal? How, precisely, would your suggested change affect the frequency response? Frequency Response
Consider numerical differentiation seen in Assignment #1 and used in an article appearing in The American Journal of Cardiology, 1991; 67: 965-975.
"Each sampled signal was differentiated according to the formula
y[n] = .5{x[n + 1] - x[n - 1]} + (1/8){x[n + 2] - x[n - 2]}
This differentiation has the convenient characteristic of shifting the frequency content of the signal upward in a precise mathematical way."
Using linear systems concepts, you can quantify the "precise mathematical way." (a) Find the the frequency response, H(e^jω).
(b) Is this discrete time system a good approximation for differentiating a continuous-time signal?
For some inputs? For all inputs? For no inputs? Explain your claim.
Hint: In the frequency domain, consider both the magnitude and phase response; recall that d dtx(t) has Fourier transform jωX(jω). Let sampling period be T seconds.
(c) How would you make this system causal? How, precisely, would your suggested change affect the frequency response?

Reference no: EM13667012

Questions Cloud

The object were on the moon rather than on the earth : 1. Would the mass density of an object be the same if the object were on the moon rather than on the earth? Would the weight density be the same?

The electric potential at the center of a square : The Electric potential at the center of a square is -2V when a charge of -q is located at one of the square's corner. What is the electric potential at the square's center when identical charges of +q are placed at the other three corner's of t..

Infinite sheet current : Infinite sheet current

What is the phase versus ? of h(e^j?) : What is the phase response for {h[n]}? That is, what is the phase versus ω of H(e^jω)?

Frequency response : Frequency Response

The embryonic origin of the anterior pituitary and posterior : Are the anterior pituitary and posterior pituitary just two of one gland or they two different glands? Relate your answers to the hormones secreted, the regulation of secretion and the embryonic origin of the anterior pituitary and posterior pi..

What ingredients negatively affect the growth of yeast : What is the worst source of energy for yeast and what ingredients negatively affect the growth of yeast?

Mother is homozygous dominant for dimples : Mother is homozygous dominant for dimples and heterozygous for curly hair and the father is heterozygous for dimples and homozygous recessive for curly hair I need the chart for this to study

Beta- galactosidase gene without losing biological function : Explain how it was possible to insert a polylinker into the 5' end of the beta- galactosidase gene without losing biological function. Also explain why biological function is almost always lost when a DNA fragment is ligated into a cut polylin..

User Account

All Pages