If you’ve hung around in audio circles long enough you’ll probably have come across 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 brand new to the term, here’s everything you need to know about frequency response.
As the name explains, we’re dealing with frequency and how well a particular component is able to reproduce all of the tones that we can hear. Human hearing ranges from very low frequencies at just 20 Hz, all the way up to very high frequencies at around 20 kHz. Although individual hearing will vary 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.
Frequency Response describes the range of frequencies or musical tones a component can reproduce.
Frequency response measures if and how well a particular audio component reproduces all of these audible frequencies and if it makes any changes to the signal on the way through. For example, what’s the lowest frequency that subwoofer X can reproduce. Barring any deliberate EQ settings, the ideal frequency output of a component should be equal to the input, so as not to alter the signal. This is often called a “flat” frequency response, where a fixed volume sine wave (measured in decibels) can be swept through the system and will be the same amplitude at all frequencies at the output.
In other words, an ideal frequency response is one that doesn’t adjust the volume of the bass, middle, or treble, from our 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 should be. In extreme cases, this can ruin the listening experience.
Problems obtaining a flat response
Unfortunately with audio, what’s ideal and what’s actually happening seldom go hand in hand—and achieving a perfectly flat frequency response across the entire audio signal chain is incredibly difficult. This is most often an issue with headphone drivers and speakers, where mechanical properties, electronics, and acoustics combine to produce non-linearity that impacts the sound. For example, impedance matching and capacitive coupling between amplifiers and speakers, speaker inductors coils and drivers, and even the acoustics of the room you’re in can all affect the final frequency response.
Every 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.
In the real world, you’ll often see frequency response specifications quote a range of frequencies, such as 20 Hz – 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 amount of boost or cut at any point between the given frequencies, so doesn’t really reveal anything about how a product will sound.
For most people, plus or minus 3 dB is considered the lower limits of what you can hear—so small deviations of 1 or 2dB here and there aren’t anything to be concerned about. But multiple deviations 3 dB or above highlights some perceivable alteration to your music. Resonant frequencies, which appear as notable isolated humps on a frequency chart, can be particularly problematic, as certain musical notes and tones then become exaggerated or masked.
Therefore, it’s not enough to look at a frequency response figure like 20Hz-20kHz +/- 3dB, it’s better to be able to see where these swings in emphasis occur and how they are distributed. A smoother frequency response is better than a highly variable one, with flat being the ideal target.
When it comes to DACs, the output should always be almost completely flat across audible frequencies, even in modern 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 a little bit trickier, but generally speaking: even an average DAC/Amp combo should have a flat frequency response when powering all but the lowest impedance speakers/headphones.
While headphone speaker components may exhibit wide variations in frequency response, DAC and amplifier components should be flat.
Fourier analysis and your music
So far, we’ve dealt with a rather easy to grasp aspect of of frequency response: that 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.
In musical instruments, these sine waves are predominantly harmonically related, occuring 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 volume. Other instruments have different harmonic relationships which partly produce their unique sound. The diagram below shows the frequency relationship differences between the sound of a piano and a violin to serve as an example.
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 harmonics leads to dull sounds lacking in space, 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 an engineer will have put into carefully mixing a track.
Why frequency response is important
By the traditional standards of HiFi, a good 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, through 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 very large impact on how the output sounds.
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 tone and 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.