Probably, your sampling rate isn't defined at 5 kHz, but vary above the spec.
Yes, you are right! 
I have a digital oscilloscope and did the measurement how as suggested by you. Here the sketch:
// Arduino Signal Filtering Test
// Turn a LED on if filter amplitude reaches an arbitrary threshold.
// 2014
// Arduino Signal Filtering Library
// Copyright 2012-2013 Jeroen Doggen (jeroendoggen@gmail.com)
//http://jeroendoggen.github.io/Arduino-signal-filtering-library/
//http://www.schwietering.com/jayduino/filtuino/
#include <SignalFilter.h> // Filter Library
SignalFilter Filter;
int Pin8 = 8; // for sampling measurement
const int ledPin = 13; // pin that the LED is attached to
const int threshold = 512; // an arbitrary threshold level that's in the range of the analog input
/* // Variable for time measurement
unsigned long time_start; // variable for time measurement start
unsigned long time_sampl; // variable for time measurement sample
int incomingByte = 0; // sets incoming Byte to 0
*/
int data1; // variable for Analog In
int data2; // variable for filter
void setup()
{
pinMode(Pin8, OUTPUT); // for sampling measurement
pinMode(ledPin, OUTPUT); // initialize the LED pin as an output:
// Serial.begin(9600); // used only printing (debugging)
Filter.begin();
Filter.setFilter('c'); // filter settings: c=Cebycheff b= Bessel
Filter.setOrder(2); // filter settings: order 1 or 2
}
/*
Filter characteristics are stored in: “SignalFilter.cpp”.
Current filter settings and code: for “c” “2”
/// runChebyshev: Band Pass 220Hz; 1. Order; lower corner =215Hz; upper corner 225Hz; sampling=5000Hz; long type 8bit; enabled "-1 bit saturation";
_v[0] = _v[1];
_v[1] = _v[2];
long tmp = ((((data * 3360365L) >> 8) //= ( 6.2591678898e-3 * x)
+ ((_v[0] * -4141801L) >> 1) //+( -0.9874824279*v[0])
+ (_v[1] * 4009861L) //+( 1.9120508347*v[1])
)+1048576) >> 21; // round and downshift fixed point /2097152
_v[2]= (short)tmp;
return (short)((
(_v[2] - _v[0]))); // 2^
*/
void loop()
{
// Read Analog Input... you can connect accelerometer, gyro, temperature sensor, microphone etc to the channel
data1 = analogRead(0)-512; //Read Analog channel (value of microphone) and substract DC-Offset from Microphone "BOB-09964"
data2 = Filter.run(data1); //Read the filtered signal
/*
http://arduino.cc/en/Tutorial/IfStatement
the variable called data1 is used to store the data collected from a Analog Pin A0.
This data is then compared to a threshold value.
If the the value is found to be above the set threshold the LED connected to digital pin 13 is turned on.
If analogValue is found to be < threshold, the LED remains off. */
// if the filter value is high enough, turn on the LED:
if (data2 > threshold) {
digitalWrite(ledPin, HIGH);
}
else {
digitalWrite(ledPin,LOW);
}
digitalWrite(Pin8, HIGH); // PIN Output High Sample Measurement
digitalWrite(Pin8, LOW); // PIN Output Low Sample Measurement
/* // time measurement for debugging:
time_start = micros(); //time measurement
data1 = analogRead(0); // for Analog Pin A0
data2 = Filter.run(data1); // for filter calculation
time_sampl = micros() - time_start; //time measurement math
if (Serial.available() > 0) {
incomingByte = Serial.read();
if (incomingByte == 'm') { // enter and sent "m" in serial monitor window and read time in microsec for Filter.run(data1) and analog read
Serial.print("Time Sample = ");
Serial.println(time_sampl, DEC);
}
} */
}
It gives me a frequency between 6,350 KHz and 6,579KHz (attachment).
On my other sketch (filter and sine wave) the sample rate is about 5,9KHz
Are there possibilities to control the sampling frequency?
