TFD

let xn=[
  {index:0,value:0},
  {index:1,value:1},
  {index:2,value:0},
  {index:3,value:-1},
  {index:4,value:0},
  {index:5,value:1},
  {index:6,value:0},
  {index:7,value:-1},
];
let X = TFD(xn);
let xk = xn.map(d=>({index:d.index,value:X(d.index)}));
console.log(xk.map(d=>Math.round(d.value*1000)/1000));

function TFD(input){
  let Z=2*Math.PI/input.length;
  let notNulls=input.filter(d=>d.value!=0);
  function X(k){
    let cosSum = notNulls.reduce((acc,d)=>(acc+Math.cos(Z*d.index*k)*d.value),0);
    let sinSum = notNulls.reduce((acc,d)=>(acc+Math.sin(Z*d.index*k)*d.value),0);
    return Math.sqrt(cosSum*cosSum+sinSum*sinSum);
  }
  return X;
}