Every sound you hear in a movie, a song, or a phone call has been shaped by audio effects — filters that cut unwanted noise, reverb that simulates the acoustics of a concert hall, pitch shifts that raise or lower a voice. In this post, we'll build all of these from scratch using Wolfram Language, turning a Mathematica notebook into a mini audio workstation.

What Is an Audio Effect?

An audio effect is any transformation applied to a sound signal. At its core, every effect is a mathematical operation on a list of numbers.
Effects fall into three broad categories:
◼
  • Time-domain effects — modify the signal directly (amplification, reversal, trimming)
    • ◼
  • Frequency-domain effects — target specific frequencies (filters, equalization)
    • ◼
  • Composite effects— combine multiple operations (reverb, noise removal)
    • Wolfram Language has built-in functions for all of these. Let's start simple and build up.

    Setting Up

    We'll use the built-in audio samples throughout this post. Let's load a few we'll need:
    bird=ExampleData[{"Audio","Bird"}];​​piano=ExampleData[{"Audio","Piano"}];​​drums=ExampleData[{"Audio","Drums"}];

    Time-Domain Effects

    These are the simplest effects — operations applied directly to the audio signal without analyzing its frequency content.

    Volume Control (Amplification)

    Changing the volume is literally multiplying every sample by a number:
    Double the volume
    loud=AudioAmplify[bird,2]
    Out[]=
    00:00
    00:02
    Data in File[
    ...93408e567669.wav
    ]
    Half the volume
    quiet=AudioAmplify[bird,0.5]
    Out[]=
    00:00
    00:02
    Data in File[
    ...bda770a4970.wav
    ]
    Mute
    silent=AudioAmplify[bird,0]
    Out[]=
    00:00
    00:02
    Data in File[
    ...97487b52c6b.wav
    ]

    Reversing Audio

    Playing audio backwards is as simple as reversing the list of samples:
    reversed=AudioReverse[bird]
    Out[]=
    00:00
    00:02
    Data in File[
    ...-253f39b2f9bf.wav
    ]

    Trimming and Joining

    segment1=AudioTrim[bird,{0,1}]​​segment2=AudioTrim[piano,{0,1}]
    Out[]=
    00:00
    00:01
    Data in File[
    ...6c85ebaa7aa.wav
    ]
    Out[]=
    00:00
    00:01
    Data in File[
    ...d9a3db20db9.wav
    ]
    Join them sequentially
    combined=AudioJoin[segment1,segment2]
    Out[]=
    00:00
    00:02
    Data in File[
    ...3cd33ebb045f.wav
    ]

    Fading In and Out

    Abrupt starts and stops sound harsh. Fading smooths the transitions:
    Fade in over the first 0.5 seconds
    fadeIn=AudioFade[bird,{0.5,0}]
    Out[]=
    00:00
    00:02
    Data in File[
    ...85375da773e.wav
    ]
    Fade out over the last 0.5 seconds
    fadeOut=AudioFade[bird,{0,0.5}]
    Out[]=
    00:00
    00:02
    Data in File[
    ...878dc5b7daa.wav
    ]
    Fade in and out
    fadeBoth=AudioFade[bird,{0.5,0.5}]
    Out[]=
    00:00
    00:02
    Data in File[
    ...208636baf0ec.wav
    ]
    A fade multiplies the beginning or end of the signal by a ramp that goes from 0 (silence) to 1 (full volume), creating a smooth transition.

    Pitch Shifting

    Pitch shifting changes how high or low a sound is without changing its speed.
    Shift up by 4 semitones
    higher=AudioPitchShift[bird,Quantity[4,"Semitones"]]
    Shift down by 4 semitones
    lower=AudioPitchShift[bird,Quantity[-4,"Semitones"]]
    Out[]=
    00:00
    00:02
    Data in File[
    ...892c9b6dfe08.wav
    ]
    Out[]=
    00:00
    00:02
    Data in File[
    ...f547a72594b2.wav
    ]

    Let's visualize the effect of pitch shifting on the spectrogram

    Original
    Spectrogrambird,
    
    Out[]=
    Shifted up by 7 semitones
    SpectrogramAudioPitchShift[bird,Quantity[7,"Semitones"]],
    
    You'll see the entire spectrogram shift upward — the same shapes, but at higher frequencies.

    Time Stretching

    Time stretching changes the duration of audio without affecting the pitch — the opposite problem of pitch shifting.
    Slow down to half speed (2x duration)
    slow=AudioTimeStretch[bird,2]
    Out[]=
    00:00
    00:04
    Data in File[
    ...85786e330f31.wav
    ]
    Speed up to double speed (0.5x duration)
    fast=AudioTimeStretch[bird,0.5]
    Out[]=
    00:00
    00:01
    Data in File[
    ...-8063400f408f.wav
    ]
    The factor works as a duration multiplier : 2 means twice as long (slower), 0.5 means half as long (faster).
    This is different from simply resampling — resampling would change both speed and pitch (like playing a vinyl record at the wrong RPM). Time stretching uses phase vocoders to preserve pitch while stretching time.

    Frequency Filters

    Filters are the workhorses of audio processing. They let you keep some frequencies and remove others.

    Lowpass Filter — Keep Only Low Frequencies

    A lowpass filter removes everything above a cutoff frequency. It keeps the bass and removes the treble:
    The spectrogram will be blank above 1000 Hz — all high-frequency content is gone. The bird chirps (which are mostly high-frequency) will be almost inaudible.

    Highpass Filter — Keep Only High Frequencies

    The opposite of lowpass: removes everything *below* the cutoff:

    Bandpass Filter — Keep a Frequency Range

    A bandpass filter keeps only frequencies between two cutoffs — useful for isolating a specific part of the spectrum:
    Keep only frequencies between 1000 Hz and 4000 Hz

    Bandstop (Notch) Filter — Remove a Frequency Range

    The inverse of bandpass — removes a specific range and keeps everything else:
    Remove frequencies between 2000 Hz and 3000 Hz
    This is commonly used to remove a specific hum or tone (like electrical hum at 50/60 Hz) without affecting the rest of the audio.

    Visualizing All Filters Side by Side

    Let's compare what each filter does to the frequency spectrum:
    Notice how each filter reshapes the frequency spectrum. The lowpass plot drops to silence (around -150 dB) after the cutoff — almost all the bird's energy is gone because bird chirps live at high frequencies. The highpass plot looks nearly identical to the original for the same reason: removing low frequencies barely affects a high-pitched bird. The bandpass shows a clear hump of energy in the 1000–4000 Hz range with sharp drop-offs on both sides — only the selected frequency band survives. The x-axis shows normalized frequency (0 to 0.5), where 0.5 corresponds to half the sample rate (22,050 Hz).

    Noise Removal

    Real-world audio often contains unwanted noise — hiss, hum, background chatter. Wolfram Language provides a built-in noise removal function:

    Using a Lowpass Filter (Remove High-Frequency Hiss)

    Background hiss lives in the high frequencies. A lowpass filter cuts it out:
    Remove high-frequency hiss by keeping only frequencies below 4000 Hz

    Using a Bandpass Filter (Isolate Speech)

    Human speech sits roughly between 300 Hz and 3400 Hz. A bandpass filter isolates just that range:
    Keep only the speech frequency range
    Compare Before and After
    In the denoised spectrogram, the faint background noise between speech segments should be visibly reduced — the "quiet" areas become truly quiet.

    Why Simple Filters Fall Short

    The problem is fundamental: noise and speech overlap in frequency. A bandpass filter removes everything outside the speech range, but the noise inside that range — which is most of it — survives completely.
    Real noise removal requires adaptive techniques that can distinguish noise from signal even when they occupy the same frequencies:
    ◼
  • Spectral subtraction — estimates the noise spectrum from silent segments and subtracts it from the entire signal
    • ◼
  • Wiener filtering — uses statistical properties to optimally separate signal from noise
    • ◼
  • Deep learning–based denoising — trains a neural network to learn what "clean" audio looks like and reconstruct it from noisy input
    These methods analyze the pattern of the noise, not just its frequency range, which is why they work far better than a simple filter.
    • It's important to understand why the simple approach has limits — it motivates the need for more sophisticated signal processing.

    Convolution Reverb — Simulating Real Spaces

    Reverb is the effect of sound bouncing off walls in a room. Different rooms produce different reverb: a bathroom sounds different from a cathedral.
    Convolution reverb works by using a recording of a real room's acoustic response — called an impulse response (IR). The built-in example library includes several:
    Load an impulse response
    Apply reverb
    Compare spectrograms
    In the reverb version, you'll see the energy "smear" in time — each sound event decays gradually instead of stopping abruptly, because the church walls reflect the sound for several seconds.
    Let's try a few different spaces:
    Listen to each one — the same bird sounds completely different in a church, a tunnel, and a 5000-year-old tomb.

    Building an Effects Chain

    In real audio production, effects are applied in sequence — one after another. Let's build a complete effects chain:
    Step 4: Add church reverb
    Step 5: Normalize volume
    Step 6: Fade in and out
    We've taken a simple bird chirp and created something that sounds like a mysterious, low-pitched call echoing through a stone church — all in 6 lines of processing.
    Let's visualize the before and after:
    Comparing the two spectrograms side by side, the transformation is clear: the original shows bright, high-frequency chirps spread across nearly 2 seconds, while the processed version is shorter, shifted lower in pitch, confined within the 500–5000 Hz band, and softened by reverb tails that trail each sound event.
    Every audio effect you hear in music, film, or a phone call boils down to mathematical operations on a list of numbers — and as we've seen, each of those operations can be expressed in a single, readable function call, taking you from raw audio to a fully processed, reverb-soaked, pitch-shifted result in minutes.

    CITE THIS NOTEBOOK

    Building an audio effects pipeline in Wolfram language​
    by Jana Rusrus​
    Wolfram Community, STAFF PICKS, March 13, 2026
    https://community.wolfram.com/groups/-/m/t/3660024