Digital Signal Processor (DSP) based 1/f α noise generator. R. Mingesz, P. Bara, Z. Gingl and P. Makra. Department of Experimental Physics, University of ...
Digital Signal Processor (DSP) based 1/f α noise generator R. Mingesz, P. Bara, Z. Gingl and P. Makra Department of Experimental Physics, University of Szeged, Hungary Dom ter 9., Szeged, H-6720 Hungary Keywords: 1/f noise, noise generator, DSP, digital filter
ABSTRACT 1/f noise is present in several natural and artificial systems, and even though it was discovered several years ago, it is still not completely understood. Due to the lack of an universal model, the main methods of investigating a system where 1/f noise is present are numerical simulations and real measurements. The second method can lead to more adequate results, since it is free from numerical artifacts. In the case of real measurements, we need reliable, wide-band noise generators. Many ways of generating noise are known; most of them have several limitations on the frequency bandwidth or on spectral properties. We wanted to create a device which is easy to use, which can generate any kind of 1/f α noise and whose bandwidth is wide enough to make our investigations. We used a DSP (ADSP2181) to numerically generate the desired noise, and a D/A converter to convert it to an analogue signal. The noise generation algorithm was based on the known method of filtering a Gaussian white noise with a series of first-order digital filters. We enhanced this method to get a better spectral shape and to compensate for the side effects of the digital-to-analogue conversion.
1. INTRODUCTION High-performance and reliable noise generators are useful to aid system analysis, system simulation, exploring time and frequency structure of different kinds of noises and many more. Nowadays computer simulation is a widely used and accepted method to generate, use and analyse noise, since sophisticated random generation and other algorithms are available. However, in real world applications it is often necessary to have an analogue noise source, like in system analysis and when the experiment has real components requiring analogue input signals. Furthermore, the limited performance of numerical methods may degrade speed and accuracy, therefore noise generators with analogue output have many potential applications. There are many ways to realise noise generators. It is quite easy and straightforward to design a white noise generator with flat spectrum, however realising a high-performance, wide frequency range 1/f α noise source is still a challenge, mainly due to the absence of a simple generation method. There are many ways to make a 1/f α noise generator [1-3]. One may use a real physical process, like semiconductor (e.g. MOSFET) noise, may apply cascaded or paralleled analogue filters to white noise or use the so-called mixed signal design (both analogue and digital), where a digital computer is used to make a pseudo-random sequence and a precision digital-to-analogue converter provides a real analogue signal. All methods have some drawbacks, like limited frequency range, absence of easily scaled frequency range and even more probably the impossibility of easy setting of the desired power exponent α. Digital methods have many advantages to address these points, but a general-purpose computer – although it may be very fast - is not optimised for real-world applications, since it may be loaded by unpredictable network traffic, background processing, etc. A very efficient solution is the use of a special-purpose digital signal processor (DSP) [3], which has very accurate timing and an extremely efficient processing core. Advanced DSPs and development tools are widely available; therefore it is quite reasonable to use a DSP to build an efficient and flexible noise generator. In this paper we show a realisation of a 1/f α noise source based on a fixed-point ADSP-2181 DSP microcomputer [4]. Our design incorporates a precision digital-to-analogue converter and an easily configurable software to aid simple setting of the frequency range and the exponent α. The noise generator is capable of providing accurate 1/f α noise over more than four decades of frequency, allows manual or host computer (typically PC) controlled setting of parameters via its standard serial interface.
2. 1/f α NOISE GENERATION USING DIGITAL FILTERS Digital filters model analogue filters and have very similar characteristics, only digital filters are used to transform data sequences that are discrete in time. For a discrete data sequence xi , the output of a digital filter is given by Eq. 1.
R
yi = D1⋅ xi + D0 ⋅ xi −1 − C 0 ⋅ yi −1 (1)
C
1
Amplitude [au]
Amplitude [au]
1
0.1
0.01
0.1
0.01
1E-3
Fm/2 0.01
0.1
1
10
1E-4 0.01
100
Frequency [Hz]
0.1
1
10
100
1000
Frequency [Hz]
Fig. 1. Analogue filter versus digital filter. On the right panel, we can see the realisation and the transfer characteristics of an analogue low-pass filter, while the left panel shows the same for the corresponding digital filter. The curves come from theoretical calculations; the sampling frequency is 1000 Hz.
The operation of the analogue and digital filters can be linked through the Bilinear Z transformation. Without going into too much detail, we should like to note that since the operation range of the digital filter is limited to the 0≤f
