## Deploying legacy analog filters to Arm Cortex-M processor cores

In recent years, major microcontroller IC vendors such as: ST, NXP, TI, ADI, Atmel/Microchip, Cypress, Maxim to name but a few have based their modern 32-bit microcontrollers on Arm’s Cortex-M processor cores. This exciting trend means that algorithms traditionally undertaken in expensive DSPs (digital signal processors) can now be integrated into a powerful low-cost and power efficient microcontroller packed full of a rich assortment of connectivity and peripheral options.

For many IC vendors, the coupling of DSP functionality with the flexibility of a low power microcontroller, has allowed them to offer their customers a generation of so called 32-bit enhanced microcontrollers suitable for a variety of practical applications. More importantly, this marriage of technologies has also allowed designers working on price critical IoT applications to implement complex algorithmic concepts, while at the same time keeping the overall product cost low and still achieving excellent low power performance.

## Upgrading legacy analog filters with the ASN Filter Designer

Analog filters have been around since the beginning of electronics, ranging from simple inductor-capacitor networks to more advanced active filters with op-amps. As such, there is a rich collection of tried and tested legacy filter designs for a broad range of sensor measurement applications.

ASN’s FilterScript symbolic math scripting language offers designers the ability to take an existing analog filter transfer function and transform it to digital with just a few lines of code. The ASN Filter Designer’s Arm automatic code generator analyses the designed digital filter and then automatically generates Arm CMSIS-DSP compliant C code suitable for direct implementation a Cortex-M based microcontroller.

### Arm CMSIS-DSP software framework

The Arm CMSIS-DSP (Cortex Microcontroller Software Interface Standard)  software framework is a rich collection of over sixty DSP functions (including various mathematical functions, such as sine and cosine; IIR/FIR filtering functions, complex math functions, and data types) developed by Arm that have been optimised for their range of Cortex-M processor cores. The framework makes extensive use of highly optimised SIMD (single instruction, multiple data) instructions, that perform multiple identical operations in a single cycle instruction. The SIMD instructions (if supported by the core) coupled together with other optimisations allow engineers to produce highly optimised signal processing applications for Cortex-M based micro-controllers quickly and simply.

## Mathematically modelling an analog circuit

Consider the active pre-emphasis filter shown below. The pre-emphasis filter has found particular use in audio work, since it is necessary to amplify the higher frequencies of the speech spectrum, whilst leaving the lower frequencies unaffected. The R and C values shown are only indented for the example, more practical values will depend on the application.A powerful method of reproducing the magnitude and phases characteristics of the analog filter in a digital implementation, is to mathematically model the circuit. This circuit may be analysed using Kirchhoff’s law, since the sum of currents into the op-amp’s inverting input must be equal to zero for negative feedback to work correctly – this results in a transfer function with a negative gain.

Therefore, using Ohm’s law, i.e. $$I=\frac{V}{R}$$,

$$\displaystyle\frac{X(s)}{R_3}=-\frac{U(s)}{C_1||R_2 + R_1}$$

After some algebraic manipulation, it can be seen that an expression for the circuit’s closed loop gain may be expressed as,

$$\displaystyle\frac{X(s)}{U(s)}=-\frac{R_3}{R_1}\frac{\left(s+\frac{1}{R_2C_1}\right)}{\left(s+\frac{R_1+R_2}{R_1R_2C_1}\right)}$$

substituting the values shown in the circuit diagram into the developed transfer function, yields

$$\displaystyle H(s)=-10\left(\frac{s+1000}{s+11000}\right)$$

### What sampling rate do we need?

Analysing the cut-off frequencies in $$H(s)$$, we see that the upper frequency is at $$11000 rad/sec$$ or $$1.75kHz$$. Therefore, setting the sampling rate to $$16kHz$$ should be adequate for modelling the filter in the digital domain.

The sampling rate options are avaliabe in the main filter design UI  (shown on the left).

### ASN FilterScript

$$H(s)$$ can be easily specified in FilterScript with the analogtf function, as follows:

Nb={1,1000};
Na={1,11000};

Ha=analogtf(Nb,Na,-10,"symbolic");


Notice how the negative gain may also be entered directly into function’s argument. The symbolic keyword generates a symbolic transfer function representation in the command window.

Applying the Bilinear z-transformation via the bilinear command with no pre-warping, i.e.

Hd=bilinear(Ha,0,"symbolic");

Notice how the bilinear command automatically scales numerator coefficients by -1, in order to account for the effect of the negative gain. The complete code is shown below:

Main()

Nb={1,1000};
Na={1,11000};

Ha=analogtf(Nb,Na,-10,"symbolic");
Hd=bilinear(Ha,0,"symbolic");

Num=getnum(Hd);
Den=getden(Hd);
Gain=getgain(Hd);


A comparison of the analog and discrete magnitude and phase spectra is shown below. Analysing the spectra, it can be seen that for a sampling rate of 16kHz the analog and digital filters are almost identical! This demonstrates the relative ease with which a designer can port their existing legacy analog designs into digital.

## Automatic code generation to Arm Cortex-M processors

As mentioned at the beginning of this article, the ASN filter designer’s automatic code generation engine facilitates the export of a designed filter to Cortex-M Arm based processor cores via the CMSIS-DSP software framework. The tool’s built-in analytics and help functions assist the designer in successfully configuring the design for deployment.

Before generating the code, the H2 filter (i.e. the filter designed in FilterScript) needs to be firstly re-optimised (transformed) to an H1 filter (main filter) structure for deployment. The options menu can be found under the P-Z tab in the main UI.

All floating point IIR filters designs must be based on Single Precision arithmetic and either a Direct Form I or Direct Form II Transposed filter structure. The Direct Form II Transposed structure is advocated for floating point implementation by virtue of its higher numerically accuracy.

Quantisation and filter structure settings can be found under the Q tab (as shown on the left). Setting Arithmetic to Single Precision and Structure to Direct Form II Transposed and clicking on the Apply button configures the IIR considered herein for the CMSIS-DSP software framework.

### Arm CMSIS-DSP application C code

Select the Arm CMSIS-DSP framework from the selection box in the filter summary window:

The automatically generated C code based on the CMSIS-DSP framework for direct implementation on an Arm based Cortex-M processor is shown below:

As seen, the automatic code generator generates all initialisation code, scaling and data structures needed to implement the IIR via the CMSIS-DSP library. This code may be directly used in any Cortex-M based development project – a complete Keil MDK example is available on Arm/Keil’s website. Notice that the tool’s code generator produces code for the Cortex-M4 core as default, please refer to the table below for the #define definition required for all supported cores.

 ARM_MATH_CM0 Cortex-M0 core. ARM_MATH_CM4 Cortex-M4 core. ARM_MATH_CM0PLUS Cortex-M0+ core. ARM_MATH_CM7 Cortex-M7 core. ARM_MATH_CM3 Cortex-M3 core. ARM_MATH_ARMV8MBL ARMv8M Baseline target (Cortex-M23 core). ARM_MATH_ARMV8MML ARMv8M Mainline target (Cortex-M33 core).

The main test loop code (not shown) centres around the arm_biquad_cascade_df2T_f32() function, which performs the filtering operation on a block of input data.

## What have we learned?

The ASN Filter Designer provides engineers with everything they need in order to port legacy analog filter designs to a variety of Cortex-M processor cores.

The FilterScript symbolic math scripting language offers designers the ability to take an existing analog filter transfer function and transform it to digital (via the Bilinear z-transform or matched z-transform) with just a few lines of code.

The Arm automatic code generator analyses the designed digital filter and then automatically generates Arm CMSIS-DSP compliant C code suitable for direct implementation on a Cortex-M based microcontroller.

### Extra resources

1. Step by step video tutorial of designing an IIR and deploying it to Keil MDK uVision.
2. Implementing Biquad IIR filters with the ASN Filter Designer and the Arm CMSIS-DSP software framework (ASN-AN025)
3. Keil MDK uVision example IIR filter project
4. Step by step instruction video of this tutorial Arm Webinar (requires registration)

## The sensor measurement challenge

Sensors come in all type of shapes and forms…There are sensors for audio, pressure, temperature, weight, strain, light, humidity…the list is almost endless.

The challenge for most, is that many sensors used in these IoT measurement applications require filtering in order to improve the performance of the sensor’s measurement data in order to make it useful for analysis.

Before jumping into the disussion, let’s first have a look at what sensor data really is….

All sensors produce measurement data. These measurement data contain two types of components:

• Wanted components, i.e. information what we want to know
• Unwanted components, measurement noise, 50/60Hz powerline interference, glitches etc – what we don’t want to know

Unwanted components degrade system performance and need to be removed.

So, the challenge for every designer is first to identify what aspects of the data we want to keep, i.e. ‘the wanted components’ and what we need to filter out, the so called ‘unwanted components’. After establishing what need to be filtered out, the challenge then which domain do we tackle this problem in, i.e. the analog domain or in the digital domain ? Each domain has its pros and cons, as we will now discuss for a practical classic sensor measurement challenge using a loadcell.

A classic sensor measurement challenge using a loadcell is shown below.

Looking at the hardware setup, we see that have a loadcell excited by a DC excitation voltage, and the general idea is that the sensor’s differential bridge voltage is amplifier by the instrumentation amplifier (IA) when strain is applied.

For those of you unfamiliar with this type of technology, a loadcell is a strain measurement sensor that is comprised of 4 strain gauges, it’s also referred to as a Wheatstone bridge, hence the terminology bridge sensor.

Analysing the signals in the schematic, we see that the differential voltage is passed through 2 filters in order to remove powerline interference and reduce measurement noise.

### What are the challenges?

The Instrumentation amplifier (IA) has high impedance inputs, which makes it easy to connect EMI (electromagnet interference) filters to the inputs. However, any mismatches with these filters will generally degrade the instrumentation amplifier’s common-mode rejection ratio, which is undesirable.

The instrumentation amplifier usually has a large gain (100 is quite typical), so any unwanted differential voltage on the inputs will be amplified. Looking at the filters, the notch depth of the powerline cancellation (50Hz/60Hz) filter will be dependent on component tolerances, and will vary over time and with temperature…This is problematic as we’ll discuss in the following section.

Finally, any analog filter or filters will require careful PCB layout and eat up precious board space, which is undesirable for many modern devices.

## Loadcell digital – is digital any better ?

Replacing the instrumentation amplifier with a 24bit sigma-delta ADC (analog-to-digital converter), we simplify the circuitry – although many ADCs don’t tolerate high impedance at their inputs, which may be problematic for good RFI (radio frequency interference) filter design.

Nevertheless, some sigma-delta devices have an in-built 50/60Hz notch filter which simplifies the filtering requirement. Although these devices are more expensive, and the choice of sampling frequency is limited, they may be good enough for some applications.

## ASP vs DSP

So, which domain is best for solving our measurement challenge, i.e. do we use analog signal processing (ASP) or digital signal processing (DSP)? In order to answer this objectively, we need to first breakdown the pros and cons of each domain.

### Analog filters

Let’s first look at an implementation using ASP.

The most obvious advantage is that analog filters have excellent resolution, as there are no ‘number of bits’ to consider. Analog filters have good EMC properties as there is no clock generating noise. There are no effects of aliasing, which is certainly true for the simpler op-amps, which don’t have any fancy chopping or auto-calibration circuitry built into them, and analog designs can be cheap which is great for cost sensitive applications.

### Sound great, but what’s the bad news?

Analog filters have several significant disadvantages that affect filter performance, such as component aging, temperature drift and component tolerance. Also, good performance requires good analog design skills and good PCB layout, which is hard to find in the contemporary skills market.

One big minus point is that filter’s frequency response remains fixed, i.e. a Butterworth filter will always be a Butterworth filter – any changes the frequency response would require physically changing components on the PCB – not ideal!

### Digital filters

Let’s now look at an implementation using DSP.

The first impression is that a digital solution is more complicated, as seen above with the five building blocks. However, digital filters have high repeatability of characteristics, and as an example, let’s say that you want to manufacture 1000 measurement modules after optimising your filter design. With a digital solution you can be sure that the performance of your filter will be identical in all modules. This is certainly not the case with analog, as component tolerance, component aging and temperature drift mean that each module’s filter will have its own characteristics.

Digital filters are adaptive and flexible, we can design and implement a filter with any frequency response that we want, deploy it and then update the filter coefficients without changing anything on the PCB!

It’s also easy to design filters with linear phase and at very low sampling frequencies – two things that are tricky with analog.

### Sound great, but what’s the bad news?

The effect of aliasing and if designing in fixed point, finite word length issues must be taken into account, including the limitation of the ADC and DAC. As there is clock source, digital designs will produce more EMI than analog filters.

## Conclusion

When designing modern IoT sensor measurement applications, digital filters offer a greater degree of design flexibility and high repeatability of characteristics over their analog counterparts.

With the advent of modern processor technology and design tooling, it is estimated that about 80% of IoT smart sensor devices are currently deployed using digital devices, such as Arm’s Cortex-M family. The Arm Cortex-M4 is a very popular choice with hundreds of silicon vendors, as it offers DSP functionality traditionally found in more expensive DSPs. Implementation is further simplified by virtue of ASN’s strong partnership with Arm who together provide a rich offering of easy to use filter design tooling and a free DSP software framework (CMSIS-DSP). These tools and well documented software framework allow you to get your IoT application up and running within minutes.