2. A signal r, t) is passed through a linear filter whose impulse response is he)....
(b) (5 pts) Unit Impulse. Suppose we have an impulse train signal h(t)-Σ δ(t-nT). Given an arbitrary signal r(t), find r(t)h(t) and (t) h(t) in terms of r(t) Show that r(t)h(t)-Σ r(nT)δ(t-nT) and r(t) * h(t)-Σ r(t-nT) (b) (5 pts) Find the Fourier Transform of r(t) (t 2n). Hint: Find wo and the Fourier series coefjicients then use the Fourier Transform property for periodic signals. (b) (5 pts) Unit Impulse. Suppose we have an impulse train signal h(t)-Σ δ(t-nT). Given...
Question 5 (a) The impulse response of a discrete-time filter is given as, hin) 0.56n-1] +n-2)0.56 n -3]. i. Derive the filter's frequency response; 11. Roughly sketch the filter's magnitude response for 0 ii. Is it a low-pass or high-pass filter? Ω 2m; (b) A continuous-time signal se(t) is converted into a discrete-time signal as shown below. s(t) is a unit impulse train. s(t) x,) Conversion into x(1) __→ⓧ一ㄅㄧ-discrete-time sequence ー→ xu [n] The frequency spectrum of ap (t) is...
Problem 6.15 The received signal in an on-off keyed digital communication system is given by (t)n(t) 1 sent n(t) 0 sent where n is AWGN with PSD σ2-N0/2, and s(t)-A(1-14)1(-1,11 (t), where A > 0, The received signal is passed through a filter with impulse response h(t).) to obtain z(t)(yh)(t) Remark: It would be helpful to draw a picture of the system before you start doing the calculations (a) Consider the decision statistic Z z(0) 1). Specify the conditional distribution...
The input r(t) to a DSBSC receiver is a DSB signal s(t) = A m(t)cos (21fet) corrupted by additive white Gaussian noise with two-sided power spectral density N,/2, where No = 10-12 W/Hz, m(t) is a message signal bandlimited to 10 kHz. Average power of m(t) is Pm = 4 W and Ac = 2 mV. The block diagram of the receiver is shown below. Note that the receiver has filters which have slightly larger bandwidths than a typical DSB...
Problem 2 Consider a general QAM scheme with transmitted symbol s(t) R { pulse shape p()71(7,/2). a(n) Apr(t - nT) exp (j2 fet)}, where the t-T./2 Let the constellation be a(n)e {2,-2,2j,-2j,0. 1. What is the appropriate matched filter to apply for this signal. Draw the optimum receiver 2. What is the average energy of the constellation, i.., E,? 3. Assume the the received signal is r(t)= s(t) +n(t), where n(t) is AWGN with variance 1. Find the error probability...
3. A white Gaussian noise signal W (t) with autocorrelation function it passes through a linear filter invariant in time h (t). Calculate the average power of the exit process Y (t) knowing that We were unable to transcribe this imager. h2 (t)dt = 1. r. h2 (t)dt = 1.
(a) Given the following periodic signal a(t) a(t) -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 i. [2%) Determine the fundamental period T ii. [5%] Derive the Fourier series coefficients of x(t). iii. [396] Calculate the total average power of z(t). iv. [5%] If z(t) is passed through a low-pass filter and the power loss of the output signal should be optimized to be less than 5%, what should be the requirement of cutoff frequency of the low-pass filter?...
5 pts D Question 1 A system has the following impulse response: .2 Sample number, n From the choices below, select the frequency response of this system. H (eju)-e(1.5 ) (2 sin( 1.5ώ) + 4 sin(0.δώ)) H (ee) = e-j(1.5e-5) (cos( 1.5 ) +2 cos(0.54)) @ H (ee)-e-n1.si) (sin( 1.54) t. 2 sin(0.δώ)) (sin(l.50) +4sin(0.0) H (ee)-e-j(1.5i) (2 cos( 1.5ώ) + 4 cos(0.5a)) H (efo)-e-n1.5u) (cos( 1.50) + 2 cos(0.50)) https://rmitinstructure.comcoursesy 5 pts DQuestion 2 A system has the following...
QUESTION 28 3 points Save The Siter coefficients of a second-order digital IR filter are: ao-1,a1-2, a2-2, bo-1. b1-1/2, b2 1/8. (a's are numerator coetficients and b's are the denominator coefficients). Determine the value of the impulse response N4? QUESTION 29 6 points Save Answer An image is to be sampled with a signal-to-quantisation ratio of at least 55 dB. The image samples are non-negative. The image sample values fall within the range from 0 to 1. How many bits...
Question 2 (50 points]: Continuous-Time Signals Given the following continuous-time signal (t). (t) 5t (a) [4%] What is the fundamental period (i.e., T) and fundamental frequency (ie, wo) of (+)? (b) [8%] Calculate the time average, average power and total energy of x(t). Is x(t) an energy signal? Explain. (c) [8%] Calculate the Fourier series coefficients of (t), i.e., {x}. [Hint: You can make use of the result in Q1(a).] (d) [8%] What is the percentage of power loss if...