Frequency-domain thinking makes filtering easier than time-domain

Evidence

Equations A1.9 and A1.10 are known as the Fourier transform pair and can be used on any type of signal, whether periodic or nonperiodic. Together, they form a powerful basis for analyzing and processing signals, in particular, because it is easier to consider filtering in the frequency domain rather than the time domain. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2766

Categorization

Category: Factual Claims

• XREF: Connects to the convolution theorem’s claim that filters multiply in the frequency domain — the practical payoff of the whole transform framework the reader needs.

Related

• Certain processes are far easier to analyze in the frequency domain than in time (similarity 0.92)
• Filtering operates as multiplication in the frequency domain, a key spectral analysis technique (similarity 0.90)
• The Fourier transform trades costly time-domain convolution for simple frequency-domain multiplication (similarity 0.89)
• Frequency, phase, and impulse responses are interchangeable transforms of each other (similarity 0.87)
• Time-frequency transforms make signal processing and interpretation easier (similarity 0.85)
• Filtering in the frequency domain is simply multiplicative on spectra (similarity 0.84)
• Filters and the signal’s time response are physically coupled tradeoffs (similarity 0.82)
• The Fourier transform pair converts signals between time and frequency domains (similarity 0.82)
• Filtering and resonance are more naturally understood in the frequency domain. (similarity 0.82)
• A filter’s time response is set by its bandwidth, not its center frequency (similarity 0.81)
• Filtering a signal distorts its time response as well as its spectrum (similarity 0.81)
• Filtering a signal to narrow its bandwidth necessarily spreads it in time. (similarity 0.79)
• Real signals contain smooth distributions of infinite frequencies (similarity 0.79)
• The ear’s analysis resembles Fourier frequency decomposition of sound (similarity 0.79)
• Any continuous signal decomposes into sinusoidal partials and convolution simplifies in frequency domain (similarity 0.79)