• AccurateRip
• Acoustid
• AES/EBU
• AirPlay
• Amplifier
• aptX
• Audio file formats
• • AAC
  • AIFF
  • ALAC
  • APE
  • DSD
  • DXD
  • FLAC
  • MP3
  • MQA
  • M4A
  • WAV
  • WMAL
• ASRC
• AVB
• Bit perfect jitter
• Bits: 16 or 24
• Bit perfect playback
• Bitrate
• Bluetooth
• Burn-in
• BWF
• Cables
  • Analog
  • Speaker
  • Bi-wiring
  • Digital
• CDtext
• Chromecast
• Clipping
• Clock
• Codec
• Compression
• CRC
• Crossover
• Cue sheet
• DAC
• Damping
• DASH
• Digital
• Digital Room Correction
• Dither
• DLNA
• Drivers
  • ASIO
  • Direct Sound
  • Kernel Streaming
  • WASAPI
  • Wave Out
• DoP
• DSP
• EBU R128 (loudness)
• FFT
• FireWire
• Freedb
• Gapless playback
• Generation loss
• HDMI
• Headphone listening
• Hearing
  • Single-sided deafness
  • Hard of hearing
• Hires recording
• Homeplug
• I2S
• ID3
• Inter sample peak
• LDAC
• Linearity (DAC)
• Memory playback
• Music Server
• OCF
• OFC
• PCM
• Perception
• RAID
• ReplayGain
• Ripping
• RFI
• RIAA
• Router
• Sampling, up and over
• Sample Rate Conversion
• Speakers
  • Driver design
  • Crossover
  • Amplification
  • Connecting
  • Measurement
  • Placement
• S/PDIF
• Storage
• Sync
• Tagging
• Toslink
• Transcoding
• UAA
• Units
• UPnP
• USB
• VST
• WiFi
• WiSA

Fast Fourier Transform

Audio is a complex signal.
It is a mix of different frequencies.
A Fourier Transform can decompose this signal in individual frequencies.
Likewise if you sum these individual frequencies you get the original sound.

The fast Fourier transform (FFT), is a computer algorithm that computes the discrete Fourier transform much faster than other algorithms

 

FFT graphs are used to display the frequency content of a small sample.

It displays the frequency content (Hz) and the intensity in dB.

You can analyze the performance of a DAC using FFT.

Send a 11 kHz test signal to the DAC and analyze the frequency content of the analog out.

 

TFFT (Temporal Frequency Analysis) plots the frequencies over time.

A color intensity scale represents the intensity of the frequency.

Demo

Paul Falstad wrote an applet demonstrating how very different functions like a triangle or a square can be generated from a sum of cosine terms.

 

References

1. The Fundamentals of FFT-Based Audio Measurements in SmaartLive - Paul D. Henderson
2. Fast Fourier transform - WikipediA
3. WavePad FFT Sound Analyzer - NCH
4. Mastering The Fourier Transform in One Day - Bernsee
5. Fourier applet - Paul Falstad