APPENDIX 01 – CAPTURING A SIGNAL WITH DIFFERENT SAMPLING RATES

 

APPENDIX 01 – CAPTURING A SIGNAL WITH DIFFERENT SAMPLING RATES

 

Introduction:

Consider a pure sine tone signal of frequency 3.999KHz. This signal will be acquired with different sampling rates. The sampling rates are 8KHz, 16KHz and 48KHz. The Nyquist theorem states that in order to capture a signal accurately, it has to be sampled at twice the signal frequency. However, practically it has to be sampled 2.5 times the signal frequency accounting for the roll-off of the anti-aliasing filter. The sampling frequencies 16KHz and 48KHz in this example satisfy the Nyquist criteria while 8KHz does not since it is not 2.5 times 3.999KHz. But the goal here is to demonstrate how the software interpolates and reconstructs the signal based on the available data points. Signal frequency of 3.999KHz is chosen instead of 4KHz so that it is possible to use 8KHz sampling rate in the software for demonstration purposes.

Graphs:

Time signal graphs of 3.999KHz with different sampling rates (zoomed for more clarity)

3.999KHz acquired with 8KHz sampling rate:

3.999KHz acquired with 16KHz sampling rate:

3.999KHz acquired with 48KHz sampling rate:

 

Quadratic Residue Diffuser (QRD)

Quadratic Residue Diffuser

Introduction

Diffusion in Acoustics is the even spreading of sound energy in a given environment. The purpose of sound diffusion is to even out the live and dead spots in a room where waves would continue to reflect upon their same paths. A Diffuser reflects sound in an even and predictable manner unlike a room with hard reflecting surfaces which would not do this. A Diffuser does not remove sound energy but radiates the sound energy in many directions leading to a live sounding space. One of the widely used diffusers is the Quadratic Residue Diffuser (QRD).

The N7 Diffuser

An N7 QRD (with 7 wells) has the following sequence 0, 1, 4, 2, 2, 4, 1. The deepest well is the well with sequence ‘4’ and the shallowest well is the well with sequence ‘0’. The deepest well value can be chosen in the design stage which further limits on the lowest diffusible frequency. As the well position ‘0’ leads to a residue of ‘0’, the well depth is also ‘0’. This is true for diffusers of any order (N5, N7, …). So, either the well ‘0’ is left as it is or it is split along the edges as shown in Figure.1. RPG Acoustical systems, a well-known manufacturer of QRD N7 diffuser, splits the ‘0’ well along the edges.

Figure 1 RPG QRD-734

QRDude Calculations

Let us consider an N7 QRD with maximum well depth to be ~97mm which translates to a design frequency of ~1000Hz. The goal is to find out what is the difference between the well ‘0’ on one side of diffuser making it unsymmetric versus splitting the well ‘0’ along edges making it symmetric.

Figure 2 N7 QRD unsymmetric well distribution

 

Figure 3 N7 QRD symmetric well distribution

 

Observations

There is no significant change observed by leaving well ‘0’ as it is on one side or splitting it along edges. Also note that if well ‘0’ were to be neglected for some reason, the diffuser still needs an ‘End Fin’ on both sides to make it meaningful and in this process one has just ‘added’ the split well ‘0’ approximately on both sides!

 

QRD Video

To learn in depth about QRD, please watch the video on YouTube by clicking the link below:

https://youtu.be/AFWoLPVw9oo