#### Signals

questions

The following function V(s) is the Laplace Transform of a voltage waveform v(t), V(s)=\frac{V_{m}}{s^{2} R C(1+s R C)} where Vm is a voltage, R is a resistance and C is a capacitance. a) Express V(s) in partial fractions. Check your answer and verify that the units areconsistent. (b) Based on the partial fraction expansion you derived in 2a, write a time-domain expression for v(t). Check your answer and verify that the units are consistent.

Match each signal a (t) to the corresponding time reversal y(t).

Part 4: Is there any visible light source that would make you perceive the can as being bright with dark letters (i.e., that makes the lettering on the can appear to be darker than the red background of the can)? Answer yes or no.

Given the following function, F(s)=\frac{4}{1+0.02 s+0.01 s^{2}}, Show that its poles are complex conjugate. Calculate the undamped natural frequency wo and the damping ratio of the poles.

c)the measured intensity for soil is highest in which visible band? A) redB)greenC)blue

6) Find the zero-state response for the following. \begin{array}{l} h[n]=(0.3)^{n} u[n] \\ x[n]=(0.1)^{n} u[n] \end{array}

3. (10 pt) The input to a subwoofer loudspeaker is to pass through a passive low-pass Butterworth filter having a cutoff frequency of 100 Hz. Specify (Design) a filter that meets the following specifications: At 50 Hz, the signal magnitude ratio should be at least at 0.95; at 200 Hz, the magnitude ratio should be no more than 0.08. The sensor and load resistances are 10 Q. Determine the minimum filter stage that satisfies the above specifications and the values for the components. Draw the corresponding electric circuit using capacitor, inductor, and resistance.

h) the best range of wavelengths for distinguishing dry land (soil+vegetation) from water areas is (choose one): visible light (400-700nm) or infrared (700-1200nm).Enter either visible or infrared.

Question 4: Cascaded Gaussians (10 pts) Define the row vector G = [1 1], which we claim approximates an unnormalized Gaussian smoothing kernel with a standard deviation of 1 / 2. Also, define the notation |G|^n to mean kernel Gconvolved with itself n-1 times. That is, |G|^2 = G*G, and |G|^3 = G*G*G, and soon. on.A) (8 pts) Fill in the values for the blanks in the following table. If the value is an nteger, enter an integer value, otherwise round to 2 decimal places.