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#include <Wire.h>
#include <Adafruit_Sensor.h>
#include <Adafruit_ADXL345_U.h>
#include <avr/io.h>
#include <avr/power.h>


#define F_CPU 16000000UL


volatile int sensor_update=0;


//-----------------------------------------------------------------------------------     -----------
//Write to ADXL345 registers
void writeTo(int device, byte address, byte val) {
Wire.beginTransmission(device); //start transmission to device
Wire.write(address);        // send register address
Wire.write(val);        // send value to write
Wire.endTransmission(); //end transmission
}



//----------------------------------------------------------------------------------------------

/////////////////////////////////////////////////////////////////////////////////////////////

//ISR function

void interrupt(void){
sensor_update=1;
  
}


//////////////////////////////////////////////////////////////////////////////////////////////////



void buzz(int targetPin, long frequency, long length) {
long delayValue = 1000000/frequency/2; // calculate the delay value between     transitions
//// 1 second's worth of microseconds, divided by the frequency, then split in half since

  //// there are two phases to each cycle
  //// calculate the number of cycles for proper timing
  long numCycles = frequency * length/ 1000; 

  //// multiply frequency, which is really cycles per second, by 
  //// the number of seconds to get the total number of cycles to produce
  for (long i=0; i < numCycles; i++){ // for the calculated length of time...
    digitalWrite(targetPin,HIGH); // write the buzzer pin high to push out the diaphram
    delayMicroseconds(delayValue); // wait for the calculated delay value
    digitalWrite(targetPin,LOW); // write the buzzer pin low to pull back the diaphram
    delayMicroseconds(delayValue); // wait againf or the calculated delay value
  }
}


/* Assign a unique ID to this sensor at the same time */
Adafruit_ADXL345_Unified accel = Adafruit_ADXL345_Unified(12345);

void setup(void)
{
  if (F_CPU == 16000000) clock_prescale_set(clock_div_1);
  Serial.begin(9600);
  //Serial.println("Accelerometer Test"); Serial.println("");

  pinMode(4, OUTPUT);// buzzer output pin
 
  /* Initialise the sensor */
  if(!accel.begin())
  {
    /* There was a problem detecting the ADXL345 ... check your connections */
    //Serial.println("Ooops, no ADXL345 detected ... Check your wiring!");
    while(1);
  }

  /* Set the range to whatever is appropriate for your project */
  accel.setRange(ADXL345_RANGE_16_G);
  accel.setDataRate(ADXL345_DATARATE_100_HZ);
  // displaySetRange(ADXL345_RANGE_8_G);
  // displaySetRange(ADXL345_RANGE_4_G);
  // displaySetRange(ADXL345_RANGE_2_G);
 
  //Create an interrupt that will trigger when a tap is detected.
  attachInterrupt(0, interrupt, RISING);
 
  writeTo(0x1D, 0x2E, 0);
  writeTo(0x1D, 0x2F, 0);
  writeTo(0x1D, 0x2E, 128);
  writeTo(0x1D, 0x2F, 127);
}

void loop(void)
{
  /* Get a new sensor event */
  interrupt();

  if(sensor_update==1 ){
    //When sensor_update is set to 1 in the ISR,the algorithm process the data from the accelerometer being updated every 10ms(100Hz)
     sensor_update=0;//reset
  }
}  

#include <Wire.h>
#include <Adafruit_Sensor.h>
#include <Adafruit_ADXL345_U.h>
#include <avr/io.h>
#include <avr/power.h>


#define F_CPU 16000000UL


volatile int sensor_update=0;


//-----------------------------------------------------------------------------------     -----------
//Write to ADXL345 registers
void writeTo(int device, byte address, byte val) {
Wire.beginTransmission(device); //start transmission to device
Wire.write(address);        // send register address
Wire.write(val);        // send value to write
Wire.endTransmission(); //end transmission
}



//----------------------------------------------------------------------------------------------

/////////////////////////////////////////////////////////////////////////////////////////////

//ISR function

void interrupt(void){
sensor_update=1;
  
}


//////////////////////////////////////////////////////////////////////////////////////////////////



void buzz(int targetPin, long frequency, long length) {
long delayValue = 1000000/frequency/2; // calculate the delay value between     transitions
//// 1 second's worth of microseconds, divided by the frequency, then split in half since

  //// there are two phases to each cycle
  //// calculate the number of cycles for proper timing
  long numCycles = frequency * length/ 1000; 

  //// multiply frequency, which is really cycles per second, by 
  //// the number of seconds to get the total number of cycles to produce
  for (long i=0; i < numCycles; i++){ // for the calculated length of time...
    digitalWrite(targetPin,HIGH); // write the buzzer pin high to push out the diaphram
    delayMicroseconds(delayValue); // wait for the calculated delay value
    digitalWrite(targetPin,LOW); // write the buzzer pin low to pull back the diaphram
    delayMicroseconds(delayValue); // wait againf or the calculated delay value
  }
}


/* Assign a unique ID to this sensor at the same time */
Adafruit_ADXL345_Unified accel = Adafruit_ADXL345_Unified(12345);

void setup(void)
{
  if (F_CPU == 16000000) clock_prescale_set(clock_div_1);
  Serial.begin(9600);
  //Serial.println("Accelerometer Test"); Serial.println("");

  pinMode(4, OUTPUT);// buzzer output pin
 
  /* Initialise the sensor */
  if(!accel.begin())
  {
    /* There was a problem detecting the ADXL345 ... check your connections */
    //Serial.println("Ooops, no ADXL345 detected ... Check your wiring!");
    while(1);
  }

  /* Set the range to whatever is appropriate for your project */
  accel.setRange(ADXL345_RANGE_16_G);
  accel.setDataRate(ADXL345_DATARATE_100_HZ);
  // displaySetRange(ADXL345_RANGE_8_G);
  // displaySetRange(ADXL345_RANGE_4_G);
  // displaySetRange(ADXL345_RANGE_2_G);
 
  //Create an interrupt that will trigger when a tap is detected.
  attachInterrupt(0, interrupt, RISING);
 
  writeTo(0x1D, 0x2E, 0);
  writeTo(0x1D, 0x2F, 0);
  writeTo(0x1D, 0x2E, 128);
  writeTo(0x1D, 0x2F, 127);
}

void loop(void)
{
  

  if(sensor_update==1 ){
    //When sensor_update is set to 1 in the ISR,the algorithm process the data from the accelerometer being updated every 10ms(100Hz)
     sensor_update=0;//reset
  }
}  

edit:

I have configured the accelerometer to have a data rate of 100Hz. I have set up an interrupt with data_ready to run the algorithm present in the loop each time a new sample comes that is each 10ms. However each sample is coming every 2ms which shows the interrupt is not working and I would like to know why. I have timed the interrupt with the millis(); function before and after calling the interrupt, also I have stored the samples in an array and printed it on the serial interface and the samples were repeated as it was updated every 2ms instead of 10ms. The algorithm I have developed needs the sampling rate to be 100Hz.