In multichannel analysis, if an interfering signal has a period T' that is slightly different from the desired signal's period T, what happens to the interfering signal's 'bump' over time?
Explanation
This question explains *how* signal averaging acts as a filter. Signals that are not at the correct frequency (period) do not add up coherently in the same memory channels. Instead, their contribution is smeared across all channels over a long enough time, effectively filtering them out.
Other questions
What is the fundamental goal of the bandwidth-narrowing techniques discussed in section 15.12?
According to section 15.12, why is simply using a low-pass filter to average out noise often an ineffective strategy?
What is the primary function of a Multichannel Scaler (MCS) as described in section 15.13?
In the signal-to-noise computation for an MCS, the signal is recognizable when the total signal counts are comparable to what quantity?
In the numerical example for an MCS where the signal contributes 10 pulses (ns) and the background contributes 1000 pulses (nb) per sweep, what is the signal-to-noise ratio after 1000 sweeps?
How does the signal-to-noise ratio improve as a function of time 't' during signal averaging?
What is the relationship between accumulating data for a time 't' in multichannel analysis and the effective measurement bandwidth, Δf?
According to section 15.14, what is a necessary prerequisite for all signal-averaging schemes to achieve a significant reduction in the signal-to-noise ratio?
What is the basic circuit for a linear phase detector used in lock-in detection, as shown in Figure 15.37?
In a lock-in amplifier, the averaged output voltage for an input signal of the same frequency as the reference is proportional to what?
What is the primary purpose of using a 'fast modulation' (e.g., at 100Hz) in the lock-in detection method?
In lock-in detection, what determines the final, narrow bandwidth of the measurement?
What is the functional difference between a Pulse-Height Analyzer (PHA) and a Multichannel Scaler (MCS)?
What is the primary application of a Pulse-Height Analyzer (PHA) in nuclear and radiation physics, according to section 15.16?
According to section 15.16, why do all PHAs use a Wilkinson converter (a variation of single-slope conversion) for their ADC front end?
What is the function of a Time-to-Amplitude Converter (TAC) as described in section 15.17?
A student using a TAC and a PHA to measure muon lifetime accumulates data for 18 days to determine a lifetime of 2.198 plus/minus 0.02 microseconds. Why was such a long data accumulation time necessary?
What does a swept-tuned spectrum analyzer display, as described in section 15.18?
How does a swept-tuned spectrum analyzer work, according to the description in section 15.18?
What is a significant disadvantage of a swept spectrum analyzer mentioned in section 15.18?
Which of the following is described as a technique for real-time spectral analysis?
What advantage does a real-time spectrum analyzer based on FFT have over a swept analyzer for low-frequency signals?
What is a 'boxcar integrator' as described in section 15.13?
When using lock-in detection with a small sinusoidal modulation, what is the output signal from the phase-sensitive detector proportional to?
What condition is necessary to make a signal periodic for averaging, using the example of generating a clean waveform of a nerve fiber's depolarization pulse?
What is an acousto-optic spectrometer or 'Bragg cell'?
What is the consequence of sweeping the local oscillator too fast in a swept spectrum analyzer?
What is the common name for a 'computer of averaged transients' or 'CAT'?
In the Mossbauer resonance example in Figure 15.35, the signal is described as 'totally swamped by noise' even after 100 sweeps. After how many sweeps does it become visible?
What is the basic assumption for all the bandwidth narrowing methods described, such as signal averaging and lock-in detection?
In the context of the lock-in amplifier demonstration with an LED and a phototransistor, what happens when the fluorescent room lights are turned on?
For a lock-in amplifier, if the post-detection low-pass filter has a time constant 'τ', what is the approximate condition for a signal with a frequency difference Δω relative to the reference to be heavily attenuated?
How is a multichannel scaler (MCS) adapted to perform signal averaging on analog signals?
What is the primary challenge when trying to measure the signal from an intrinsically periodic source like a pulsar, as mentioned in section 15.14?
In the Crab nebula pulsar measurement, what was the average number of detected photons for each entire pulsar pulse?
What is the key advantage of digital Fourier analysis (FFT) based spectrum analyzers over swept analyzers?
What is the effect of using a large square-wave modulation in lock-in detection, as opposed to a small sine wave?
What does the term '1/f noise' refer to?
In the context of a phase detector, if the time constant of the low-pass filter is τ = RC and the period of the reference signal is T = 2π/ω, what must be the relationship between them for proper averaging?
What is the main reason that analog signal averagers like the boxcar integrator are becoming impractical, according to section 15.13?
For the Mossbauer resonance example in section 15.13, what were the approximate values for the signal counts per sweep (ns) and background counts per sweep (nb)?
According to the signal-to-noise computation on page 1029, the signal amplitude improves proportionally to the square root of time 't'. How many decibels (dB) of improvement does this correspond to for each doubling of 't'?
What does a real-time spectrum analyzer based on a 'chirp/Z transform' use in place of the standard IF bandpass filter found in a swept-LO analyzer?
Why must the sweep rate be kept slow when scanning with a narrow bandwidth on a swept spectrum analyzer?
Which of these is NOT listed as a technique of bandwidth narrowing in widespread use?
What is the key functional component inside a Multichannel Scaler (MCS)?
If a poor input signal-to-noise ratio is characterized by the signal pulse rate 'ns' being much less than the background pulse rate 'nb' (ns << nb), what does this imply for a single sweep of an MCS?
The overall effect of long data accumulation in a lock-in amplifier experiment using modulation frequency fmod and total time T is to do what?
What is 'off-line spectrum analysis' as described in section 15.19?