If possible, provide a mathematically defined signal with the following properties. If no such signal exists, explain why not.
An aperiodic anticausal signal z(t) that has power Pz=e
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If possible, provide a mathematically defined signal with the following properties. If no such signal exists,...
Determine if there exists a linear transformation T: R2 -> R2
with the following properties.
If yes, give an example. If no, explain why such a
transformation is not possible.
(4) Determine if there exists a linear transformation T: R2 + R2 with the following properties. If yes, give an example. If no, explain why such a transformation is not possible. (a) T is one-to-one and onto. (b) T is not one-to-one. (c) T is not onto. (d) T is...
Consider the following waveform f(t) which is a one cycle of a sinusoid for 0 seconds while zero elsewhere (Aperiodic Signal) 2- t π in fo) 0 -10 a) Represent f(t) mathematically. b) Determine the Laplace transform using the integral expression c) Repeat that using the properties of the Laplace transform
Question 1: The following system gets its input signal g(t) and convolve it with a train of deltas d(t) g(t) d(t) ſ(t) 1-1 Find the Fourier transform ( Gw) or G(f) ) for the aperiodic signal g(t) 1-2 Find the Fourier series coefficients, Dn for the periodic signal g(t) if d(e) = į 8(t - 4n) N -00 1-3 Plot the frequency spectrum for GW) 1-4 Find the average power of the periodic g(t) Question 1: The following system gets...
A Random Telegraph Signal with rate λ > 0 is a random process X(t) (where for
each t, X(t) ∈ {±1}) defined on [0,∞) with the following properties: X(0) = ±1
with probability 0.5 each, and X(t) switches between the two values ±1 at the
points of arrival of a Poisson process with rate λ i.e., the probability of k changes
in a time interval of length T isP(k sign changes in an interval of length T) = e
−λT...
b.) Find the unilateral Laplace transform of the signal z(t) defined as follows x(t) = [e-5* u(t)] * [(t – 2) ult – 2)]
3. Let Vi is AC input signal which has following properties: Voffset: 1 Volt Vpp: 0.5 Volt Waveform: Sinus Frequency: 1 KHz a) Why we chose 1 Volt for offset voltage? b) If the waveform is Square, what would happens in terms of circuit characteristics? How do you make AC Analysis of the circuit to calculate expected output signal? Please explain as step by step. R2-820 0 c) (NPN) R1-100 Figure 1. A transistor circuit
3. Let Vi is AC...
2. (30 points) Let X(t) be a wide-sense stationary (WSS) random signal with power spectral density S(f) = 1011(f/200), and let y(t) be a random process defined by Y(t) = 10 cos(2000nt + 1) where is a uniformly distributed random variable in the interval [ 027]. Assume that X(t) and Y(t) are independent. (a) Derive the mean and autocorrelation function of Y(t). Is Y(t) a WSS process? Why? (b) Define a random signal Z(t) = X(t)Y(t). Determine and sketch the...
(a) Use the tables of transforms and properties to find the FT's of the following signal: [2 sin(37t) sin(2t) x(t) TTT Tt = 2[sin(270]
3. The system represented by the block diagram below modulates the message signal x(t) with a carrier wave c(t) to yield -(). The signal y(t) is generated by multiplying z() by the carrier wave c(t). c(t) c(t) y(t) z(t) The output signal,y(t), can be written as y(t)-C() × X() x C(t). Using the properties of a) Fourier Transforms, write Yi) in terms of Cjo) and Yj). [2 points] The Fourier Transform of x(t) is illustrated below. 0.9 0.8 0.7 0.6...
3) (Fourier Transforms Using Properties) - Given that the Fourier Transform of a signal x(t) is X(f) - rect(f/ 2), find the Fourier Transform of the following signals using properties of the Fourier Transform: (a) d(t) -x(t - 2) (d) h(t) = t x( t ) (e) p(t) = x( 2 t ) (f) g(t)-x( t ) cos(2π) (g) s(t) = x2(t ) (h)p()-x(1)* x(t) (convolution)
3) (Fourier Transforms Using Properties) - Given that the Fourier Transform of a signal...