On Inter-Sample Peaks¶

In digital audio, the term inter-sample peak is used to refer to clipping of a digital audio signal that can occur when:

The digital audio signal is scaled in amplitude without regard to the analog signal that it represents, and
That digital audio signal is converted to a different sample rate.

This page will explain what an inter-sample peak (ISP) is, how it occurs, and how they are handled in the miniDSP 2x4 HD.

A brief explanation of ISPs¶

Figure 1 shows an analog signal in blue and a possible digital sampling of it in red.

Illustration of inter-sample peaks, Figure 1 — Figure 1

This artificial signal won't occur in real music but it's useful to explain the concept. If the sample rate is 44.1 kHz, the figure shows one cycle of an 11.025 kHz sine wave. The maximum allowable levels of the digital signal are +1 and -1, and the digital samples have the value 0.707 or -0.707.

In digital music production, it's common to try and maximize the digital signal level. If this is done in a simple manner with the signal shown above, the result is as shown in Figure 2.

Illustration of inter-sample peaks, Figure 2 — Figure 2

Each sample has been scaled up to have a value of +1 or -1. They are still within the digital range. However, the analog signal that this digital stream now represents has sections that exceed the +/-1 limit. The peaks in this underlying analog signal are referred to as the true peaks. The true peak is marked in Figure 2. For a more detailed discussion, see the BBC Whitepaper Terminology for Loudness and Level dBTP, LU and all that.

If this digital signal is then converted to a different sample rate, some of the new samples will be over the digital limit. This is illustrated in Figure 3.

Illustration of inter-sample peaks, Figure 3 — Figure 3

Since they are over the digital limit, however, they cannot be represented correctly and will clip. The signal we end up with is shown in Figure 4, which has a lot of distortion.

Illustration of inter-sample peaks, Figure 4 — Figure 4

The clipped samples in Figure 4 are referred to as inter-sample peaks. (The term is not quite accurate, but we use it as it's commonly used for this phenomenon. By convention, true peak is the actual peak value of the underlying analog waveform, and inter-sample peaks are the sample that exceed the digital limit after sample-rate conversion and are therefore clipped.) ISP's are also called "inter-sample overs."

ISPs with music signals¶

While the previous section used an artificial signal to illustrate the concept of ISPs, they also occur with music signals. The amount by which the true peaks of a music signal exceed the digital maximum depends on the music and the way that it was processed digitally. For example, the author of the web page What are inter-sample peaks and true peaks? has measured true peaks up to 2.4 dB over the digital limit.

It's possible that clipped inter-sample peaks are less of an issue with modern recordings, due to increased awareness of the issue in music production and greater availability of production tools that are able to measure the true peak of a digital audio track.

It's also worth also noting that most streaming services require that music uploaded to them has a maximum true peak of -1 or -2 dB. (The 1 or 2 dB headroom is to allow for errors when the music is streamed via a lossy encoding process.) The web page Mastering for Streaming: Platform Loudness and Normalization Explained, for example, lists the maximum allowed true peak – shown as e.g. -1 dBTP – of several services.

How ISPs are handled¶

As explained above, ISPs become an issue when the sample rate of a full-scale digital audio signal is changed. Most modern DAC chips oversample their incoming audio stream, and are thus susceptible to distortion from ISPs.

In the miniDSP 2x4 HD, while the internal digital processing uses floating-point arithmetic and is therefore not subject to the digital limit until the output to the DAC, it also has an integer-based asynchronous sample rate convertor (ASRC) at the input stage.

Our solution to ISPs in the 2x4 HD is to change the gain structure right at the input stage. The digital input signal is attenuated by 3 dB before it enters the ASRC. After the ASRC, the digital signal is increased in level by 3 dB.

This avoids introducing ISPs with most recorded material that has true peaks exceeding the digital limit. For example, the article linked above found true peaks up to 2.4 above, although higher is certainly possible.