Signals Homework Help

2. (21 pts) Given the general properties listed in Problem #1, determine which ones hold and which ones do not hold for the following discrete-time systems. Justify your answers. Like before, y[n] denotes system output and r[n] is the system input.

1. A continuous-time signal x(t) is shown in Figure below. Sketch and label carefully each of the following signals: (а) x(- 1) (b) x(2- t) (c) x(2t + 1)

C. (1 pts) Let NCC be the value of the normalized correlation score computedbetween patches f and g. Circle the equation below that best describes the valueof NCC. Note that these are mutually exclusive ranges, so only choose one. 1) NCC = -1 2) -1 < NCC <0 3) NCC = 0 4) 0 < NCC <1 5) NCC = 1

2. (10 pt) Design a cascading LC low-pass filter with maximally flat magnitude response.Use a passband of 0 to 5 kHz with 5 kHz cutoff frequency and filter to attenuate all frequencies at and above 10 kHz by at least 30 dB. The source and load resistances are 50N. Specify the number of stages (select an integer number close the calculated value k)and the values for the components.

3.25. Consider the following three continuous-time signals with a fundamental period of T = 1/2: x(t)=cos(4nt), y(t) =sin(4nt), z(t) = x(t)y(t). (a) Determine the Fourier series coefficients of x(t). (b) Determine the Fourier series coefficients of y(t). (c) Use the results of parts (a) and (b), along with the multiplication property of the continuous-time Fourier series, to determine the Fourier series coefficients of z(t) = x(t)y(t). (d) Determine the Fourier series coefficients of z(t) through direct expansion of z(t)in trigonometric form, and compare your result with that of part (c).

\text { 2. }(36 \text { pts }) \text { Let } u(t)=\frac{1}{1+(2 \pi t)^{2}} \text { and } v(t)=e^{-|t|} \text {. Express all answers with both an exact analytic expression } and a decimal approximation. (a) Find the smallest frequency bands that contain 90%, 99%, and 99.9% of the energy of u. Do the same for v. (b) Find the frequency bands where |U(f)|2 is at least c times the maximum value of |U(f)|² forcE {0.1,0.01, 0.001}. Do the same for V.

4. (10 pt) A transducer measuring pressure needs to respond to oscillations up to 3 Hz but iscontaminated by 60 Hz noise. To reduce the 60 Hz noise, a student wants to design a lowpass Butterworth filter having a passband of 0 to 3 Hz with 3 Hz cutoff frequency. 4-1) (5pt) If the student wants to attenuate all frequencies at and above 10 Hz by at least30 dB, what is the required number of filter stages? Determine the minimum number of the filter stage. 4-2) (5pt) If the filter stage determined by 4-1) is used, how much is the amplitude of the60 Hz noise attenuated? How much is the amplitude of the 60 Hz noise attenuated if the student uses a first order low-pass Butterworth filter?

Problem 4. For each pole-zero plot below, determine the following system properties: 1. Is the system stable and does the DTFT exist? 2. Is the system causal? 3. Write H(z)as a ratio of two polynomials corresponding to the poles and zeros.

f) In which visible band are water and soil most distinguishable, that is, the intensity values are least similar? Enter red, green or blue.

Q3) The results of a slotted-line experiment are plotted in the following figure. The length of the line is & cm; its characteristic impedance is Z0 Q. a) The reflection coefficient at the load. b) The load impedance. c) The input impedance. d) The reflection coefficient at the generator terminals.