Exercise 34.1 Suppose the filter A: equation '(R) '(R) is governed 2 (a) Compute its impulse response. (b) Compute and represent graphically the step response. Exercise 34.1 Suppose t...
a The impulse response of a filter is given by h(t) = where a, b, and to are positive constants. (t-to)2+b2 (a) Find the transfer function and absolute bandwidth of the filter. (b) Find the 5-dB bandwidth of the filter. (c) Find the 95% essential bandwidth of the filter. (d) Find the equivalent bandwidth of the filter.
a) The transfer function of an ideal low-pass filter is and its impulse response is where oc is the cut-off frequency i) Is hLP[n] a finite impulse response (FIR) filter or an infinite impulse response filter (IIR)? Explain your answer ii Is hLP[n] a causal or a non-causal filter? Explain your answer iii) If ae-0. IT, plot the magnitude responses for the following impulse responses b) i) Let the five impulse response samples of a causal FIR filter be given...
aliasing? A continuous-time system is given by the input/output differential equation 4. H(s) v(t) dy(t) dt dx(t) + 2 (+ x(t 2) dt (a) Determine its transfer function H(s)? (b) Determine its impulse response. (c) Determine its step response. (d) Is the stable? (a) Give two reasons why digital filters are favored over analog filters 5. (b) What is the main difference between IIR and FIR digital filters? (c) Give an example of a second order IIR filter and FIR...
2. A signal r, t) is passed through a linear filter whose impulse response is he). The output signal ro (t) of the linear filter is sampled at the symbol period of T. he signal r,(t) is given as (t)t)+n and the n(t) is the AwGN with noise variance of σ-N0/2. Note that s(t) is a complex signal. You have to show your work in detail for the full credit. n(t) where s(t) has the energy of E (a) Derive...
Please show work.
An FIR filter is described by the difference equation: (a) Find its impulse response h[n] and plot versus n. 1 n 0,2,4 0 elsewhere (b) Find the output when the input signal is n]-
A linear time invariant system has an impulse response given by h[n] = 2(-0.5)" u[n] – 3(0.5)2º u[n] where u[n] is the unit step function. a) Find the z-domain transfer function H(2). b) Draw pole-zero plot of the system and indicate the region of convergence. c) is the system stable? Explain. d) is the system causal? Explain. e) Find the unit step response s[n] of the system, that is, the response to the unit step input. f) Provide a linear...
6 An equation that relates impulse response h and step response s is: (2 points) sh/ds Oh(t)=d/dt h(t)= ds(t)/dt O h(t)= d(ht/dt)
Problem 2 Consider an FIR filter with the following impulse response: h [n] [1 -2 3] (a) What is the gain at 2 0.67 rads/sample? (b) What is the filter output if the input is x(n] - [1 2 3 2 1? Problem 2: Consider an FIR filter with the following impulse response: h(n] [1-2 3 (a) What is the gain at 2 0.67 rads/sample? (b) What is the filter output if the input is x [n] 1 2 3...
Question 3 A filter has a unit-impulse response h(t)=0.5e-2'u(t). an (i) Find the frequency response H(jo). (ii) Determine an expression for the steady-state response of the filter to v> 02 sáng)
In each step to follow, the signals h(t), a(t), and y(t) denote respectively the impulse response, input, and output of a continuous-time LTI system. Accordingly, H(w), X(w) and Y(w) denote their Fourier transforms. Hint: Carefully consider for each step whether to work in the time domain or frequency domain. (b) (25 points) On the axes below, provide a clearly labeled sketch of y(t) for all t given Σ H(w)-( ) sine? (w/8) j2Tt r(t)-e δ(t-n/2) and with sinc(t) = sin(t)/t...