Question 37 of 50

What is the fundamental concept of Fourier analysis as it relates to real-world signals?

How is the transfer function H(f) of a two-port filter defined?

A filter has a transfer function where, at 1000 Hz, the magnitude |H(1000)| = 3 and the phase angle is 30 degrees. If the input signal is vin(t) = 2 cos(2000 * pi * t + 40 degrees), what is the output signal vout(t)?

What is the formula for the half-power frequency, fB, of a first-order RC lowpass filter?

For a first-order RC lowpass filter with a resistance R = (1000 / (2*pi)) Ohms and a capacitance C = 10 microfarads, what is the half-power frequency, fB?

How is the magnitude of a transfer function, |H(f)|, converted to its equivalent in decibels (dB)?

What is the decibel equivalent for a transfer-function magnitude of 10?

What does a 'decade' represent on a logarithmic frequency scale?

What is the slope of the high-frequency asymptote in a Bode magnitude plot for a first-order lowpass filter?

In a Bode magnitude plot for a first-order filter, what is the difference between the actual magnitude and the straight-line asymptote approximation at the corner frequency (fB)?

What is the formula for the resonant frequency, f0, of a series RLC circuit?

In the context of a series resonant circuit, how is the quality factor (Qs) defined?

A series resonant circuit has an inductance L = 159.2 mH and a capacitance C = 0.1592 microfarads. What is its resonant frequency, f0?

For a series resonant circuit with f0 = 1000 Hz, L = 159.2 mH, and R = 100 Ohms, what is the quality factor, Qs?

For a series resonant circuit with a resonant frequency f0 = 1000 Hz and a quality factor Qs = 10, what is the bandwidth B?

What are the four types of ideal filters described in the chapter?

In a Bode magnitude plot, how does the high-frequency roll-off of a second-order lowpass filter compare to a first-order lowpass filter?

What is the primary purpose of an antialias filter in a digital signal processing system?

How many decades are there between 20 Hz and 15 kHz, the approximate range of audible frequencies?

In a cascade connection of two filters with transfer functions H1(f) and H2(f), how is the overall transfer function H(f) determined?

A transfer function has a magnitude of |H(f)| = 50. What is its decibel equivalent?

For a first-order highpass filter, what is the slope of the low-frequency asymptote in its Bode magnitude plot?

A first-order RC highpass filter needs to reduce the amplitude of a 1 kHz component by 50 dB. What is the required half-power frequency (fB) for this filter?

In a parallel resonant circuit, how is the quality factor (Qp) defined in terms of its components R, L, and resonant frequency f0?

A parallel resonant circuit has a resistance R = 10 kOhms, an inductance L = 100 microhenrys, and a capacitance C = 500 picofarads. What is its resonant frequency, f0?

What is the primary characteristic of an ideal band-reject filter, also known as a notch filter?

To design a second-order highpass filter that passes components higher than 1 kHz and rejects components lower than 1 kHz, what values should be chosen for the resonant frequency f0 and quality factor Qs?

What is the primary advantage of converting transfer-function magnitudes to decibels before plotting them on a Bode plot?

A filter's transfer function magnitude is given by |H(f)| = 10 / sqrt(1 + (f/5000)^6). At what frequency is the magnitude 3 dB less than its value at very low frequencies?

What is an 'octave' on a logarithmic frequency scale?

How many octaves are there between a frequency of 5 kHz and 50 kHz?

What is the phase of a first-order lowpass filter at its half-power frequency, fB?

What is the phase of a first-order highpass filter at its half-power frequency, fB?

In a series RLC circuit at resonance, what happens to the voltages across the inductor (VL) and the capacitor (VC) if the quality factor Qs is high?

For a parallel resonant circuit with a constant current source, what is the voltage across the circuit at the resonant frequency, f0?

For a series resonant circuit with R = 2.709 Ohms and L = 2.156 microhenrys, what capacitance C is needed to achieve a resonant frequency of 5 MHz?

In the Practical Application concerning active noise cancellation, what is the primary reason this technology is attractive for use in aircraft?

What does it mean for a filter's transfer function to be -80 dB at a specific frequency?

In the straight-line approximation of a first-order lowpass filter's phase plot, at what frequency does the sloping line begin?

An input signal vin(t) = 3 + 2cos(2000*pi*t) + cos(4000*pi*t - 70 degrees) is applied to a filter whose transfer function H(f) is shown in Figure 6.4, where H(0)=4, H(1000)=3 angle 30 degrees, and H(2000)=2 angle 60 degrees. What is the DC component of the output signal?

For a first-order RC highpass filter, what happens to the magnitude of the transfer function as the frequency approaches zero?

To filter an ECG signal, an ideal highpass filter with a cutoff of 0.5 Hz is used, followed by an ideal lowpass filter with a cutoff of 100 Hz, followed by an ideal band-reject filter for 60 Hz interference. What is the purpose of the initial highpass filter?

What is the bandwidth of a series resonant filter with a resonant frequency of 5 MHz and a quality factor of 25?

For a digital filter defined by the difference equation y(n) = a*y(n-1) + (1-a)*x(n), what is the output y(0) if a=0.9, y(-1)=0, and the input x(n) is a step function where x(0)=1?

How many octaves higher than 1000 Hz is 4000 Hz?

A simple digital notch filter is described by y(n) = 0.5 * [x(n) + x(n-d)]. If the sampling frequency is 10 kHz, what value of the delay 'd' is needed to eliminate a 500 Hz component?

What is the half-power frequency of the second-order bandpass filter shown in Figure 6.37?

In the manual analysis of a complex filter circuit to check a computer-generated Bode plot, how do inductances and capacitances behave at very low (DC) frequencies?

What is the primary physical phenomenon that causes resonance in a series RLC circuit?