Frequency Response, Bode Plots, and Resonance

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?

A second-order lowpass filter is designed with Qs = 0.707. What is this type of filter response called?

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?