Arduino Uno Digital to Analog Converter

Question

I'm trying to read in an analog signal (a heartbeat) to pin A0 on the Arduino Uno and then convert it to digital. I'm hoping to use the digital signal to make an LED light up every time the voltage of the heartbeat signal goes over 1 volt. This is the code I have right now, but something is wrong because it isn't lighting up the LED.

unsigned int analog0;             // Raw data from A0 ranging from 0 to 1023
unsigned long data_range = 2000;  // Length of time to record data for
double volts;                     // The analog data from A0 converted to volts
int ledPin = 13;
unsigned long start_time;
unsigned long data_time;

void setup() {
  Serial.begin(9600);             // Initialize and set serial port baud rate
  pinMode(ledPin , OUTPUT);
}

void loop() {
  start_time = millis();    
  while ((millis() - start_time) < data_range)
  {
    // Record current time of analog acquisition
    data_time = millis();

    // Record analog data on A0
    analog0 = analogRead(0);

    // Convert raw data into voltage
    volts = (analog0 / 1023.0) * 5;

    Serial.print(volts);
    Serial.println();

    // Slow the rate of data acquisition
    //delay(1);

    if (volts > 1.5){
      digitalWrite(ledPin, HIGH);
      //delay(50);
    }
    else{
      digitalWrite(ledPin, LOW);
    }
  }     
}

Answer 1

Try commenting out the serial in your sketch. In my experience serial communication takes time, and I assume you have a short window where the voltage peaks at more than a volt. Or initialize the serial with a stupidly high baud rate.
Edit: even better, you could try this for a faster response time:

void setup(){
  digitalWrite(13,0);
  pinMode(13, OUTPUT);
}

void loop(){
  if(analogRead(A0)>204){ //at ~1V the ADC will read between 204 and 205
    digitalWrite(13,1);
    delay(100);
    digitalWrite(13,0);
  }
}

Answer 2

I think your voltage formula is wrong. Try this:

float volts = analog0 * (5.0 / 1023.0);