If you’ve hung around in audio circles long enough you’re probably aware of the term frequency response. It can crop up in pretty much any discussion, ranging from headphones and speakers right on through to DACs and amplifiers, and even room acoustics. Whether you’re familiar with the subject or if the term is brand new to you, here’s everything you need to know about frequency response.
Editor’s note: this article was updated on May 19, 2023, to update formatting and linking.
What is a frequency response?
A frequency response is a visual representation of how well an audio component reproduces the audible range of sound. It’s usually presented as a line graph, with the device’s output amplitude on the y axis (in decibels) plotted against frequency on the x-axis (in Hertz). To measure the frequency response, a fixed amplitude sine wave is swept through all the frequencies of interest while an analyzer tracks the output. In most cases, the ideal is that the system and will produce the same amplitude at all frequencies, so the output equals the input. This is often referred to as a “flat” frequency response because in this case the graph produced is a straight, horizontal line.
Frequency response can often be thought of much like a filter, which can boost or attenuate the input signal to alter the sound.
In other words, an ideal frequency response is one that doesn’t change the relative levels of the bass, middle, or treble, from the source. By comparison, if you’ve messed around with any music app’s EQ settings, you might have seen a non-flat EQ setting that boosts bass or cuts treble, etc. So if a component (such as a headphone driver) doesn’t have a flat frequency response, you may end up hearing more or less of certain frequencies than there were in the original signal. In extreme cases, this can ruin the listening experience.
Our hearing ranges from very low frequencies starting at 20 Hz, all the way up to very high frequencies at around 20 kHz (20,000 Hertz), though an individual’s hearing will fall between these two extremes. In a musical sense, we often see this split into bass, middle, and treble sections. These aren’t fixed definitions, but typically bass accounts for frequencies between 20 and 300 Hz , mid is 300 Hz to 4 kHz, and treble counts as anything above 4 kHz, very roughly speaking.
Problems obtaining a flat response
A comparison of an ideal (green), a likely imperceptible real-world example (yellow), and more audible (red) frequency responses for speakers.
Achieving a perfectly flat frequency response across the entire audio signal chain varies in difficulty depending on what kind of component we’re talking about. For example, with headphone drivers and speakers, where mechanical properties, electronics, and acoustics combine to produce non-linearities that impact the sound, it’s a big challenge. Impedance matching between amplifiers and inductive speaker components, and even the acoustics of the room you’re in all affect the final frequency response.
You’ll often see audio specifications quote a range of frequencies, such as 20Hz-20 kHz, followed by the amount of variation in the frequency response quoted in decibels, such as +/- 6 dB. This simply tells us the maximum deviation at any point between the given frequencies, so doesn’t really tell us anything about how a product will sound.
Each component in the signal chain should ideally have a flat frequency response, so that the sound passes through unaltered. But the reality is that many components don't offer ideal performance.
Generally speaking, plus or minus 3dB is considered the lower limits of what you can reliably hear—so smaller deviations of 1 or 2dB here and there aren’t anything to be concerned about. But multiple deviations 3dB or above will more likely cause some perceivable alteration to your music. Resonant frequencies, which appear as pronounced bumps on a frequency chart, can be particularly problematic, as certain musical notes and tones then become exaggerated, or masked by the resonance.
Therefore, it’s not enough to look at a spec like 20Hz-20kHz +/- 3dB, it’s better to be able to see where these swings in emphasis occur and how they are distributed. A smooth frequency response is better than a highly variable one, with flat usually considered the ideal.
While electroacoustic components can exhibit wide variations in frequency response, DAC and amplifier components should be flat.
When it comes to DACs, the output should always be almost completely flat across audible frequencies, even in low-cost designs. The conversion from digital to analog in today’s hardware is a straight sampling conversion, before filtering out the noise at frequencies well beyond human perception. There aren’t any mechanical or acoustic problems to worry about at this stage. Amplifier circuits are also pretty interchangeable as far as audible performance goes. Generally speaking: even an average DAC/Amp combo should have a flat frequency response when powering all but the lowest impedance speakers/headphones.
Fourier analysis and your music
Music producers have their work cut out for them, as changes to emphasis mean changes to sound quality overall.
So a non-linear response will alter the way our source sounds. However, this isn’t just about common concepts like bass and treble, but it also impacts the sound quality of every instrument in the mix. To get our head around this more subtle aspect of how non-linear frequency response can affect what we hear, we need to turn to Fourier analysis.
In a nutshell, Fourier analysis and the Fourier transform reveal that a complex waveform can be expressed as the sum of a series of sine waves of differing amplitudes. So a square, triangle, or any other wave shape that appears in the time domain can be represented by multiple different individual frequencies of varying amplitudes in the frequency domain.This includes the waveform shapes that are created by musical instruments, ranging from sharp beats of a snare drum through to fat square wave electric guitars.
Source: Lucas V. Barbosa, Wikimedia
In musical instruments, these sine waves are predominantly harmonically related, occurring at odd and even octaves (multiples of the fundamental note frequency) above the root note. So for example, if you play natural C on a violin, that sounds the fundamental frequency of 261 Hz, plus some second harmonic at 522 Hz, third at 783 Hz, fourth at 1044 Hz, and so on with diminishing amounts of level. Other instruments have differing relative harmonic content which creates their unique sounds. The diagram below shows the frequency relationship differences between the sound of a piano and a violin to serve as an example.
Harmonics may be quiet, but they’re no less important to your music.
Why does this matter? Well going back to frequency response and filtering, we can now see that a non-flat response not only alters the overall representation of our music, but can change the way that individual instruments sound as well. Even if a frequency response graph doesn’t present any major bass or treble issues, the smaller nonlinearities at certain frequencies can alter our perception of certain instruments.
Some general rules of equalization are that decreasing an instrument’s fundamental frequency produces a less powerful sound, while increasing it adds “depth.” Similarly, reducing an instrument’s harmonic content leads to dull and unnatural sounds, while boosting harmonics increases “presence,” but can eventually sound overly harsh. Taking this one step further, boosting and cutting different instrument frequencies may even end up masking or amplifying the sound of other instruments in the track. So a nonlinear frequency response can undo all the hard work that the engineers will have put into carefully mixing and mastering a track.
Why frequency response is important
It may not be flashy, but the Beyerdynamic DT 770 Studio is metal as hell.By the traditional standards of HiFi, an accurate audio system is one that takes an input signal and outputs it without changing it at all. This includes components ranging from the source audio file to digital processing and components like a DAC, right on out to the amplifier and speakers. Frequency response is just one part of this equation, but one that has a significant impact on how the output sounds and is coincidentally quite easy to measure.
Frequency response isn’t just about whether there’s too much bass, mid, or treble coming out of a system. It can also more subtly affect the tonal balance of instruments within a track, potentially coloring and even ruining our listening experience. A perfectly flat, ideal response isn’t possible with every component, but today’s higher-end technology can certainly come close enough that a human could never tell.
If our goal is listen to back to music in as pure a form as possible, then we have to pay attention to frequency response. It can also be a handy tool if you’re looking to EQ your way out of less than perfect hardware too.
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